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xy\\).\u003c/p\u003e","Type":true},{"ID":1225,"Answer":"\u003cp\u003eנבודד את y מהמשוואה הראשונה בעזרת הוצאת שורש: \u0026nbsp;\\(y = \\sqrt {xy - {x^2}} \\).\u003c/p\u003e","Type":false},{"ID":1226,"Answer":"\u003cp\u003eנבודד את \\({x^2}\\) מהמשוואה השנייה: \u0026nbsp;\\({x^2} = 4 - xy - {y^2}\\).\u003c/p\u003e","Type":false}],"TopicName":null,"CorrectAnswer":"\u003cp\u003eנשווה את 2 האגפים הימניים: \u0026nbsp;\\(xy = 4 - xy\\).\u003c/p\u003e","Answer1":"\u003cp\u003eנבודד את x מהמשוואה הראשונה: \u0026nbsp;\\(\\frac{{{x^2} + {y^2}}}{y} = x\\).\u003c/p\u003e","Answer2":"\u003cp\u003eנבודד את y מהמשוואה הראשונה בעזרת הוצאת שורש: \u0026nbsp;\\(y = \\sqrt {xy - {x^2}} \\).\u003c/p\u003e","Answer3":"\u003cp\u003eנבודד את \\({x^2}\\) מהמשוואה השנייה: \u0026nbsp;\\({x^2} = 4 - xy - {y^2}\\).\u003c/p\u003e","Answer4":null,"Explanation":"\u003cp\u003eבשיטת ההצבה, ניתן להחליף ביטוי בביטוי שקול לו ממשוואה אחת לאחרת.\u003c/p\u003e","Question":"\u003cp\u003eמה השלב הבא בפתרון המשוואה: \u0026nbsp;\\(\\begin{array}{l}{x^2} + {y^2} = xy\\\\{x^2} + {y^2} = 4 - 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8 = 8 - 8\\)\u003c/p\u003e","Type":false},{"ID":1086,"Answer":"\u003cp\u003e\\(3x + 2 + 4 = 8 + 4\\)\u003c/p\u003e","Type":false},{"ID":1087,"Answer":"\u003cp\u003e\\(5 \\cdot 3x + 2 = 5 \\cdot 8\\)\u003c/p\u003e","Type":true},{"ID":1088,"Answer":"\u003cp\u003e\\(\\frac{{3x + 2}}{3} = \\frac{8}{3}\\)\u003c/p\u003e","Type":false}],"TopicName":null,"CorrectAnswer":"\u003cp\u003e\\(5 \\cdot 3x + 2 = 5 \\cdot 8\\)\u003c/p\u003e","Answer1":"\u003cp\u003e\\(3x + 2 - 8 = 8 - 8\\)\u003c/p\u003e","Answer2":"\u003cp\u003e\\(3x + 2 + 4 = 8 + 4\\)\u003c/p\u003e","Answer3":"\u003cp\u003e\\(\\frac{{3x + 2}}{3} = \\frac{8}{3}\\)\u003c/p\u003e","Answer4":null,"Explanation":"\u003cp\u003eכל פעולה שמבוצעת על משוואה צריכה להיות מבוצעת על כל אגף במלואו.\u003c/p\u003e","Question":"\u003cp\u003eאילו מהמשוואות הבאות אינן שקולות למשוואה: \u0026nbsp;\\(3x + 2 = 8\\)?\u003c/p\u003e"},{"ID":185,"VideoQuestionName":"שאלה 4","VideoQuestionID":272,"VideoID":38688,"Type":"middle","TimeStampString":"00:00:01","TimeStamp":1,"OrderNumber":0,"VideoName":null,"Active":true,"VideoQuestionAnswersItems":[{"ID":1089,"Answer":"\u003cp\u003e\\(2x = 12\\)\u003c/p\u003e","Type":false},{"ID":1090,"Answer":"\u003cp\u003e\\({x^2} = 0\\)\u003c/p\u003e","Type":false},{"ID":1091,"Answer":"\u003cp\u003e\\(6x = \u0026nbsp;- x + 6\\)\u003c/p\u003e","Type":false},{"ID":1092,"Answer":"\u003cp\u003e\\(2x = 0\\)\u003c/p\u003e","Type":true}],"TopicName":null,"CorrectAnswer":"\u003cp\u003e\\(2x = 0\\)\u003c/p\u003e","Answer1":"\u003cp\u003e\\(2x = 12\\)\u003c/p\u003e","Answer2":"\u003cp\u003e\\({x^2} = 0\\)\u003c/p\u003e","Answer3":"\u003cp\u003e\\(6x = \u0026nbsp;- x + 6\\)\u003c/p\u003e","Answer4":null,"Explanation":"\u003cp\u003eבפתרון משוואה נעביר אגפים ונכנס איברים על מנת לבודד את הנעלם באגף אחד ולמצוא את פתרון המשוואה.\u003c/p\u003e","Question":"\u003cp\u003eמה השלב הבא בפתרון המשוואה: \u0026nbsp;\\(x + 6 = \u0026nbsp;- x + 6\\).\u003c/p\u003e"},{"ID":186,"VideoQuestionName":"שאלה 5","VideoQuestionID":273,"VideoID":38688,"Type":"middle","TimeStampString":"00:00:01","TimeStamp":1,"OrderNumber":0,"VideoName":null,"Active":true,"VideoQuestionAnswersItems":[{"ID":1093,"Answer":"\u003cp\u003e\\(2x - 4 = 4x + 12 - 4\\)\u003c/p\u003e","Type":false},{"ID":1094,"Answer":"\u003cp\u003e\\(2x + 4x = 12 - 4 + 4\\)\u003c/p\u003e","Type":true},{"ID":1095,"Answer":"\u003cp\u003e\\(6x = 12\\)\u003c/p\u003e","Type":false},{"ID":1096,"Answer":"\u003cp\u003e\\(x = 2\\)\u003c/p\u003e","Type":false}],"TopicName":null,"CorrectAnswer":"\u003cp\u003e\\(2x + 4x = 12 - 4 + 4\\)\u003c/p\u003e","Answer1":"\u003cp\u003e\\(2x - 4 = 4x + 12 - 4\\)\u003c/p\u003e","Answer2":"\u003cp\u003e\\(6x = 12\\)\u003c/p\u003e","Answer3":"\u003cp\u003e\\(x = 2\\)\u003c/p\u003e","Answer4":null,"Explanation":"\u003cp\u003eהעברת אגפים מתבצעת עם הפעולה הנגדית הקושרת את האיבר או הגורם לאגף. חיבור/חיסור וכפל/חילוק.\u003c/p\u003e","Question":"\u003cp\u003eרוני טעתה בפתרון למשוואה: \u0026nbsp;\\(2\\left( {x - 2} \\right) = 4\\left( {x + 3} \\right) - 4\\).\u003cbr\u003eסמנו באיזו שורה נפלה הטעות.\u003c/p\u003e"}],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[]],[[{"ID":187,"VideoQuestionName":"שאלה 1","VideoQuestionID":274,"VideoID":38664,"Type":"middle","TimeStampString":"00:00:01","TimeStamp":1,"OrderNumber":0,"VideoName":null,"Active":true,"VideoQuestionAnswersItems":[{"ID":1097,"Answer":"\u003cp\u003e(2,2)\u003c/p\u003e","Type":false},{"ID":1098,"Answer":"\u003cp\u003e(4,-4)\u003c/p\u003e","Type":true},{"ID":1099,"Answer":"\u003cp\u003e(5,1)\u003c/p\u003e","Type":false},{"ID":1100,"Answer":"\u003cp\u003e(-1,3)\u003c/p\u003e","Type":false}],"TopicName":null,"CorrectAnswer":"\u003cp\u003e(4,-4)\u003c/p\u003e","Answer1":"\u003cp\u003e(2,2)\u003c/p\u003e","Answer2":"\u003cp\u003e(5,1)\u003c/p\u003e","Answer3":"\u003cp\u003e(-1,3)\u003c/p\u003e","Answer4":null,"Explanation":"\u003cp\u003eפתרון של משוואה הוא פתרון אשר הצבתו במשוואה מניבה פסוק אמת.\u003c/p\u003e","Question":"\u003cp\u003eאיזה מהזוגות הסדורים הבאים אינו פתרון של המשוואה: \u0026nbsp;\\(3y + x = 8\\)?\u003c/p\u003e"},{"ID":188,"VideoQuestionName":"שאלה 2","VideoQuestionID":275,"VideoID":38664,"Type":"middle","TimeStampString":"00:00:01","TimeStamp":1,"OrderNumber":0,"VideoName":null,"Active":true,"VideoQuestionAnswersItems":[{"ID":1101,"Answer":"\u003cp\u003e\\(\\begin{array}{l}6x + 12y = 18\\\\6x - 2y = 16\\end{array}\\)\u003c/p\u003e","Type":false},{"ID":1102,"Answer":"\u003cp\u003e\\(\\begin{array}{l}x = 3 - 2y\\\\6x - 2y = 16\\end{array}\\)\u003c/p\u003e","Type":false},{"ID":1103,"Answer":"\u003cp\u003e\\(\\left( {x + 2y} \\right) - \\left( {6x - 2y} \\right) = 3 - 16\\)\u003c/p\u003e","Type":true},{"ID":1104,"Answer":"\u003cp\u003e\\(\\left( {x + 2y} \\right) + \\left( {6x - 2y} \\right) = 3 + 16\\)\u003c/p\u003e","Type":false}],"TopicName":null,"CorrectAnswer":"\u003cp\u003e\\(\\left( {x + 2y} \\right) - \\left( {6x - 2y} \\right) = 3 - 16\\)\u003c/p\u003e","Answer1":"\u003cp\u003e\\(\\begin{array}{l}6x + 12y = 18\\\\6x - 2y = 16\\end{array}\\)\u003c/p\u003e","Answer2":"\u003cp\u003e\\(\\begin{array}{l}x = 3 - 2y\\\\6x - 2y = 16\\end{array}\\)\u003c/p\u003e","Answer3":"\u003cp\u003e\\(\\left( {x + 2y} \\right) + \\left( {6x - 2y} \\right) = 3 + 16\\)\u003c/p\u003e","Answer4":null,"Explanation":"\u003cp\u003eבשיטת השוואת מקדמים נרצה לצמצם נעלם בעל מקדם מספרי דומה בשתי המשוואות על ידי חיבור או חיסור.\u003cbr\u003eבשיטת ההצבה נרצה לבודד ביטוי במשוואה אחת כדי להציב אותו בשנייה ובכך לצמצם את כמות הנעלמים.\u003c/p\u003e","Question":"\u003cp\u003eנתונה מערכת המשוואות: \u0026nbsp;\\(\\begin{array}{l}x + 2y = 3\\\\6x - 2y = 16\\end{array}\\).\u003cbr\u003eמה לא מתאים להיות השלב הבא בדרך לפתרון המערכת?\u003c/p\u003e"},{"ID":189,"VideoQuestionName":"שאלה 3","VideoQuestionID":276,"VideoID":38664,"Type":"middle","TimeStampString":"00:00:01","TimeStamp":1,"OrderNumber":0,"VideoName":null,"Active":true,"VideoQuestionAnswersItems":[{"ID":1105,"Answer":"\u003cp\u003e\\(\\begin{array}{l}3x + 4y = 7\\\\3x + 4y = 1\\end{array}\\)\u003c/p\u003e","Type":true},{"ID":1106,"Answer":"\u003cp\u003e\\(\\begin{array}{l}x = 3\\\\y = 4\\end{array}\\)\u003c/p\u003e","Type":false},{"ID":1107,"Answer":"\u003cp\u003e\\(\\begin{array}{l}4x + 8y = 12\\\\2x + 4y = 6\\end{array}\\)\u003c/p\u003e","Type":false},{"ID":1108,"Answer":"\u003cp\u003e\\(\\begin{array}{l}x + y = 0\\\\x - y = 0\\end{array}\\)\u003c/p\u003e","Type":false}],"TopicName":null,"CorrectAnswer":"\u003cp\u003e\\(\\begin{array}{l}3x + 4y = 7\\\\3x + 4y = 1\\end{array}\\)\u003c/p\u003e","Answer1":"\u003cp\u003e\\(\\begin{array}{l}x = 3\\\\y = 4\\end{array}\\)\u003c/p\u003e","Answer2":"\u003cp\u003e\\(\\begin{array}{l}4x + 8y = 12\\\\2x + 4y = 6\\end{array}\\)\u003c/p\u003e","Answer3":"\u003cp\u003e\\(\\begin{array}{l}x + y = 0\\\\x - y = 0\\end{array}\\)\u003c/p\u003e","Answer4":null,"Explanation":"\u003cp\u003eכאשר פתרון מערכת מביא לפסוק שקר, אין למערכת פתרון.\u003c/p\u003e","Question":"\u003cp\u003eלאיזה מערכת משוואות אין פתרון?\u003c/p\u003e"},{"ID":190,"VideoQuestionName":"שאלה 4","VideoQuestionID":277,"VideoID":38664,"Type":"middle","TimeStampString":"00:00:01","TimeStamp":1,"OrderNumber":0,"VideoName":null,"Active":true,"VideoQuestionAnswersItems":[{"ID":1109,"Answer":"\u003cp\u003e\\(3x + y = 5x - 1\\)\u003c/p\u003e","Type":false},{"ID":1110,"Answer":"\u003cp\u003e\\(3\\left( {5x - 1} \\right) + y = 7\\)\u003c/p\u003e","Type":false},{"ID":1111,"Answer":"\u003cp\u003e\\(5x - 1 = 7\\)\u003c/p\u003e","Type":false},{"ID":1112,"Answer":"\u003cp\u003e\\(3x + 5x - 1 = 7\\)\u003c/p\u003e","Type":true}],"TopicName":null,"CorrectAnswer":"\u003cp\u003e\\(3x + 5x - 1 = 7\\)\u003c/p\u003e","Answer1":"\u003cp\u003e\\(3x + y = 5x - 1\\)\u003c/p\u003e","Answer2":"\u003cp\u003e\\(3\\left( {5x - 1} \\right) + y = 7\\)\u003c/p\u003e","Answer3":"\u003cp\u003e\\(5x - 1 = 7\\)\u003c/p\u003e","Answer4":null,"Explanation":"\u003cp\u003eבשיטת ההצבה נרצה לבודד ביטוי במשוואה אחת כדי להציב אותו בשנייה ובכך לצמצם את כמות הנעלמים.\u003cbr\u003eהביטוי המוצב במשוואה אחת מוחלף בביטוי השקול לו במשוואה השנייה.\u003c/p\u003e","Question":"\u003cp\u003eנתונה מערכת משוואות: \u0026nbsp;\\(\\begin{array}{l}3x + y = 7\\\\y = 5x - 1\\end{array}\\).\u003cbr\u003eטליה רוצה לפתור את מערכת המשוואות בשיטת ההצבה.\u003cbr\u003eמה עליה לעשות בשלב הבא?\u003c/p\u003e"},{"ID":191,"VideoQuestionName":"שאלה 5","VideoQuestionID":278,"VideoID":38664,"Type":"middle","TimeStampString":"00:00:01","TimeStamp":1,"OrderNumber":0,"VideoName":null,"Active":true,"VideoQuestionAnswersItems":[{"ID":1113,"Answer":"\u003cp\u003eלכפול את המשוואה הראשונה ב-3 ואת השנייה ב-5.\u003c/p\u003e","Type":false},{"ID":1114,"Answer":"\u003cp\u003eלכפול את המשוואה השנייה ב-(2-).\u003c/p\u003e","Type":false},{"ID":1115,"Answer":"\u003cp\u003eלכפול את המשוואה השנייה ב-2.\u003c/p\u003e","Type":false},{"ID":1116,"Answer":"\u003cp\u003eלכפול את המשוואה הראשונה ב-3 ואת השנייה ב-2.\u003c/p\u003e","Type":true}],"TopicName":null,"CorrectAnswer":"\u003cp\u003eלכפול את המשוואה הראשונה ב-3 ואת השנייה ב-2.\u003c/p\u003e","Answer1":"\u003cp\u003eלכפול את המשוואה הראשונה ב-3 ואת השנייה ב-5.\u003c/p\u003e","Answer2":"\u003cp\u003eלכפול את המשוואה השנייה ב-(2-).\u003c/p\u003e","Answer3":"\u003cp\u003eלכפול את המשוואה השנייה ב-2.\u003c/p\u003e","Answer4":null,"Explanation":"\u003cp\u003eבשיטת השוואת מקדמים נרצה להביא את אותו הביטוי להיות בעל אותו המקדם המספרי בשתי המשוואות\u003cbr\u003eעל מנת לצמצם את הביטוי בעזרת חיבור או חיסור המשוואות.\u003c/p\u003e","Question":"\u003cp\u003eנתונה מערכת המשוואות: \u0026nbsp;\\(\\begin{array}{l}2x + 5y = 5\\\\x + 3y = 7\\end{array}\\).\u003cbr\u003eמה לא כדאי לעשות בשלב הבא?\u003c/p\u003e"}],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[]],[[{"ID":192,"VideoQuestionName":"שאלה 1","VideoQuestionID":279,"VideoID":38765,"Type":"middle","TimeStampString":"00:00:01","TimeStamp":1,"OrderNumber":0,"VideoName":null,"Active":true,"VideoQuestionAnswersItems":[{"ID":1117,"Answer":"\u003cp\u003e\\(3x + 2 = \u0026nbsp;- 3x + 1\\)\u003c/p\u003e","Type":false},{"ID":1118,"Answer":"\u003cp\u003e\\(x + x + 1 = 2x + 1\\)\u003c/p\u003e","Type":false},{"ID":1119,"Answer":"\u003cp\u003e\\(x - x = 4\\)\u003c/p\u003e","Type":true},{"ID":1120,"Answer":"\u003cp\u003e\\(x = \u0026nbsp;- x\\)\u003c/p\u003e","Type":false}],"TopicName":null,"CorrectAnswer":"\u003cp\u003e\\(x - x = 4\\)\u003c/p\u003e","Answer1":"\u003cp\u003e\\(3x + 2 = \u0026nbsp;- 3x + 1\\)\u003c/p\u003e","Answer2":"\u003cp\u003e\\(x + x + 1 = 2x + 1\\)\u003c/p\u003e","Answer3":"\u003cp\u003e\\(x = \u0026nbsp;- x\\)\u003c/p\u003e","Answer4":null,"Explanation":"\u003cp\u003eכאשר הנעלם מצטמצם ומתקבל פסוק שקר (מספר שווה למספר אחר), אין למשוואה פתרון.\u003c/p\u003e","Question":"\u003cp\u003eלאיזו משוואה מהמשוואות הבאות אין פתרון?\u003c/p\u003e"},{"ID":193,"VideoQuestionName":"שאלה 2","VideoQuestionID":280,"VideoID":38765,"Type":"middle","TimeStampString":"00:00:01","TimeStamp":1,"OrderNumber":0,"VideoName":null,"Active":true,"VideoQuestionAnswersItems":[{"ID":1121,"Answer":"\u003cp\u003e\\(x + x + 7 = 2x - 7\\)\u003c/p\u003e","Type":false},{"ID":1122,"Answer":"\u003cp\u003e\\(2x = x + x\\)\u003c/p\u003e","Type":true},{"ID":1123,"Answer":"\u003cp\u003e\\(x = \u0026nbsp;- x\\)\u003c/p\u003e","Type":false},{"ID":1124,"Answer":"\u003cp\u003e\\(2x - 9 = \u0026nbsp;- 2x + 9\\)\u003c/p\u003e","Type":false}],"TopicName":null,"CorrectAnswer":"\u003cp\u003e\\(2x = x + x\\)\u003c/p\u003e","Answer1":"\u003cp\u003e\\(x + x + 7 = 2x - 7\\)\u003c/p\u003e","Answer2":"\u003cp\u003e\\(x = \u0026nbsp;- x\\)\u003c/p\u003e","Answer3":"\u003cp\u003e\\(2x - 9 = \u0026nbsp;- 2x + 9\\)\u003c/p\u003e","Answer4":null,"Explanation":"\u003cp\u003eכאשר הנעלם מצטמצם ומתקבל פסוק אמת (מספר שווה לעצמו), יש למשוואה אינסוף פתרונות.\u003c/p\u003e","Question":"\u003cp\u003eלאיזו משוואה מהמשוואות הבאות יש אינסוף פתרונות?\u003c/p\u003e"},{"ID":194,"VideoQuestionName":"שאלה 3","VideoQuestionID":281,"VideoID":38765,"Type":"middle","TimeStampString":"00:00:01","TimeStamp":1,"OrderNumber":0,"VideoName":null,"Active":true,"VideoQuestionAnswersItems":[{"ID":1125,"Answer":"\u003cp\u003e\\(4x\\)\u0026nbsp;\u003c/p\u003e","Type":false},{"ID":1126,"Answer":"\u003cp\u003e\\( - 5x\\)\u003c/p\u003e","Type":false},{"ID":1127,"Answer":"\u003cp\u003e\\(3x\\)\u003c/p\u003e","Type":true},{"ID":1128,"Answer":"\u003cp\u003e\\(5x\\)\u003c/p\u003e","Type":false}],"TopicName":null,"CorrectAnswer":"\u003cp\u003e\\(3x\\)\u003c/p\u003e","Answer1":"\u003cp\u003e\\(4x\\)\u0026nbsp;\u003c/p\u003e","Answer2":"\u003cp\u003e\\( - 5x\\)\u003c/p\u003e","Answer3":"\u003cp\u003e\\(5x\\)\u003c/p\u003e","Answer4":null,"Explanation":"\u003cp\u003eכאשר הנעלם מצטמצם ומתקבל פסוק אמת (מספר שווה לעצמו), יש למשוואה אינסוף פתרונות.\u003c/p\u003e","Question":"\u003cp\u003eאיזה ביטוי צריך להכניס במקום הריק כדי שלמשוואה: \u0026nbsp;\\(4x - 2 = x - 2 + \\_\\_\\_\\) יהיו אינסוף פתרונות?\u0026nbsp;\u003c/p\u003e"}],[],[],[],[],[]],[[{"ID":195,"VideoQuestionName":"שאלה 1","VideoQuestionID":282,"VideoID":38721,"Type":"middle","TimeStampString":"00:00:01","TimeStamp":1,"OrderNumber":0,"VideoName":null,"Active":true,"VideoQuestionAnswersItems":[{"ID":1129,"Answer":"\u003cp\u003e\\(2{x^2} + 1 = 0\\)\u003c/p\u003e","Type":false},{"ID":1130,"Answer":"\u003cp\u003e\\(2x + 1 = 0\\)\u003c/p\u003e","Type":false},{"ID":1131,"Answer":"\u003cp\u003e\\(2{x^2} - x = 0\\)\u003c/p\u003e","Type":false},{"ID":1132,"Answer":"\u003cp\u003e\\(2{x^2} + x = 0\\)\u003c/p\u003e","Type":true}],"TopicName":null,"CorrectAnswer":"\u003cp\u003e\\(2{x^2} + x = 0\\)\u003c/p\u003e","Answer1":"\u003cp\u003e\\(2{x^2} + 1 = 0\\)\u003c/p\u003e","Answer2":"\u003cp\u003e\\(2x + 1 = 0\\)\u003c/p\u003e","Answer3":"\u003cp\u003e\\(2{x^2} - x = 0\\)\u003c/p\u003e","Answer4":null,"Explanation":"\u003cp\u003eבמשוואה ריבועית (\\a)\\ הוא מקדם של הנעלם בריבוע.\u003cbr\u003e(\\b)\\ הוא המקדם של הנעלם במעלה ראשונה. (\\c)\\ הוא האיבר החופשי.\u003c/p\u003e","Question":"\u003cp\u003eעבור איזה משוואה מהמשוואות הבאות מתקיים: \u0026nbsp;\\(a = 2{\\rm{ }},\\;b = 1{\\rm{ }},\\;c = 0\\)?\u003c/p\u003e"},{"ID":196,"VideoQuestionName":"שאלה 2","VideoQuestionID":283,"VideoID":38721,"Type":"middle","TimeStampString":"00:00:01","TimeStamp":1,"OrderNumber":0,"VideoName":null,"Active":true,"VideoQuestionAnswersItems":[{"ID":1133,"Answer":"\u003cp\u003e\\(\\frac{{ - 2 \\pm \\sqrt {{2^2} - 4 \\cdot 1 \\cdot 3} }}{{2 \\cdot 1}}\\)\u003c/p\u003e","Type":false},{"ID":1134,"Answer":"\u003cp\u003e\\(\\frac{{ - \\left( { - 2} \\right) \\pm \\sqrt { - {2^2} - 4 \\cdot 1 \\cdot \\left( { - 3} \\right)} }}{{2 \\cdot 1}}\\)\u0026nbsp;\u003c/p\u003e","Type":false},{"ID":1135,"Answer":"\u003cp\u003e\\(\\frac{{ - \\left( { - 2} \\right) \\pm \\sqrt {{{\\left( { - 2} \\right)}^2} - 4 \\cdot 1 \\cdot \\left( { - 3} \\right)} }}{{2 \\cdot 1}}\\)\u003c/p\u003e","Type":true},{"ID":1136,"Answer":"\u003cp\u003e\\(\\frac{{ - 2 \\pm \\sqrt {{{\\left( { - 2} \\right)}^2} - 4 \\cdot 0 \\cdot \\left( { - 3} \\right)} }}{{2 \\cdot 0}}\\)\u003c/p\u003e","Type":false}],"TopicName":null,"CorrectAnswer":"\u003cp\u003e\\(\\frac{{ - \\left( { - 2} \\right) \\pm \\sqrt {{{\\left( { - 2} \\right)}^2} - 4 \\cdot 1 \\cdot \\left( { - 3} \\right)} }}{{2 \\cdot 1}}\\)\u003c/p\u003e","Answer1":"\u003cp\u003e\\(\\frac{{ - 2 \\pm \\sqrt {{2^2} - 4 \\cdot 1 \\cdot 3} }}{{2 \\cdot 1}}\\)\u003c/p\u003e","Answer2":"\u003cp\u003e\\(\\frac{{ - \\left( { - 2} \\right) \\pm \\sqrt { - {2^2} - 4 \\cdot 1 \\cdot \\left( { - 3} \\right)} }}{{2 \\cdot 1}}\\)\u0026nbsp;\u003c/p\u003e","Answer3":"\u003cp\u003e\\(\\frac{{ - 2 \\pm \\sqrt {{{\\left( { - 2} \\right)}^2} - 4 \\cdot 0 \\cdot \\left( { - 3} \\right)} }}{{2 \\cdot 0}}\\)\u003c/p\u003e","Answer4":null,"Explanation":"\u003cp\u003eבמשוואה ריבועית (\\a)\\ הוא מקדם של הנעלם בריבוע.\u003cbr\u003e(\\b)\\ הוא המקדם של הנעלם במעלה ראשונה. (\\c)\\ הוא האיבר החופשי.\u003cbr\u003eנוסחת השורשים היא: \u0026nbsp;\\(x = \\frac{{ - b \\pm \\sqrt {{{\\left( b \\right)}^2} - 4ac} }}{{2a}}\\)\u003c/p\u003e","Question":"\u003cp\u003eבחרו בהצבה הנכונה בנוסחת השורשים של המשוואה: \u0026nbsp;\\({x^2} - 2x - 3 = 0\\)?\u003c/p\u003e"},{"ID":197,"VideoQuestionName":"שאלה 3","VideoQuestionID":284,"VideoID":38721,"Type":"middle","TimeStampString":"00:00:01","TimeStamp":1,"OrderNumber":0,"VideoName":null,"Active":true,"VideoQuestionAnswersItems":[{"ID":1137,"Answer":"\u003cp\u003e\\(x = 4\\)\u003c/p\u003e","Type":false},{"ID":1138,"Answer":"\u003cp\u003e\\(x = 4{\\rm{ }},\\;x = \u0026nbsp;- 4\\)\u003c/p\u003e","Type":true},{"ID":1139,"Answer":"\u003cp\u003e\\(x = 0{\\rm{ }},\\;x = 16\\)\u003c/p\u003e","Type":false},{"ID":1140,"Answer":"\u003cp\u003e\\(x = 8{\\rm{ }},\\;x = \u0026nbsp;- 8\\)\u003c/p\u003e","Type":false}],"TopicName":null,"CorrectAnswer":"\u003cp\u003e\\(x = 4{\\rm{ }},\\;x = \u0026nbsp;- 4\\)\u003c/p\u003e","Answer1":"\u003cp\u003e\\(x = 4\\)\u003c/p\u003e","Answer2":"\u003cp\u003e\\(x = 0{\\rm{ }},\\;x = 16\\)\u003c/p\u003e","Answer3":"\u003cp\u003e\\(x = 8{\\rm{ }},\\;x = \u0026nbsp;- 8\\)\u003c/p\u003e","Answer4":null,"Explanation":"\u003cp\u003eבהוצאת שורש מסדר זוגי כפתרון למשוואה נקבל תוצאה חיובית ושלילית אשר שתיהן מקיימות את המשוואה.\u003c/p\u003e","Question":"\u003cp\u003eמה הפתרון של המשוואה הבאה: \u0026nbsp;\\({x^2} = 16\\)?\u003c/p\u003e"},{"ID":198,"VideoQuestionName":"שאלה 4","VideoQuestionID":285,"VideoID":38721,"Type":"middle","TimeStampString":"00:00:01","TimeStamp":1,"OrderNumber":0,"VideoName":null,"Active":true,"VideoQuestionAnswersItems":[{"ID":1141,"Answer":"\u003cp\u003e\\({x^2} = 0\\)\u003c/p\u003e","Type":false},{"ID":1142,"Answer":"\u003cp\u003e\\({x^2} = \u0026nbsp;- 16\\)\u003c/p\u003e","Type":false},{"ID":1143,"Answer":"\u003cp\u003e\\( - {x^2} - 3x = 0\\)\u003c/p\u003e","Type":true},{"ID":1144,"Answer":"\u003cp\u003e\\({x^2} + 1 = 0\\)\u003c/p\u003e","Type":false}],"TopicName":null,"CorrectAnswer":"\u003cp\u003e\\( - {x^2} - 3x = 0\\)\u003c/p\u003e","Answer1":"\u003cp\u003e\\({x^2} = 0\\)\u003c/p\u003e","Answer2":"\u003cp\u003e\\({x^2} = \u0026nbsp;- 16\\)\u003c/p\u003e","Answer3":"\u003cp\u003e\\({x^2} + 1 = 0\\)\u003c/p\u003e","Answer4":null,"Explanation":"\u003cp\u003eלמשוואה ריבועית יש 2 פתרונות ממשיים שונים כאשר הדיסקרימיננטה: \u0026nbsp;\\({\\left( b \\right)^2} - 4ac\\) \u0026nbsp;חיובית.\u003cbr\u003eכאשר (\\a)\\ הוא מקדם של הנעלם בריבוע. (\\b)\\ הוא המקדם של הנעלם במעלה ראשונה.\u003cbr\u003e(\\c)\\ הוא האיבר החופשי.\u003c/p\u003e","Question":"\u003cp\u003eלאיזה מהמשוואות הבאות יש 2 פתרונות?\u003c/p\u003e"},{"ID":199,"VideoQuestionName":"שאלה 5","VideoQuestionID":286,"VideoID":38721,"Type":"middle","TimeStampString":"00:00:01","TimeStamp":1,"OrderNumber":0,"VideoName":null,"Active":true,"VideoQuestionAnswersItems":[{"ID":1145,"Answer":"\u003cp\u003e\\({x^2} = 4x\\)\u003c/p\u003e","Type":false},{"ID":1146,"Answer":"\u003cp\u003e\\(x\\left( {x - 4} \\right) = 0\\)\u003c/p\u003e","Type":true},{"ID":1147,"Answer":"\u003cp\u003e\\(x - 4 = 0\\)\u003c/p\u003e","Type":false},{"ID":1148,"Answer":"\u003cp\u003e\\( - 3x = 0\\)\u003c/p\u003e","Type":false}],"TopicName":null,"CorrectAnswer":"\u003cp\u003e\\(x\\left( {x - 4} \\right) = 0\\)\u003c/p\u003e","Answer1":"\u003cp\u003e\\({x^2} = 4x\\)\u003c/p\u003e","Answer2":"\u003cp\u003e\\(x - 4 = 0\\)\u003c/p\u003e","Answer3":"\u003cp\u003e\\( - 3x = 0\\)\u003c/p\u003e","Answer4":null,"Explanation":"\u003cp\u003eכאשר ניתן לפרק לגורמים על מנת להגיע למכפלה ששווה ל- (\\0)\\ אז ניתן לפתור את המשוואה על ידי השוואת כל גורם בנפרד\u0026nbsp;\u003cbr\u003eל-(\\0)\\.\u003c/p\u003e","Question":"\u003cp\u003eמה השלב הבא בפתרון המשוואה הבאה: \u0026nbsp;\\({x^2} - 4x = 0\\)?\u003c/p\u003e"},{"ID":200,"VideoQuestionName":"שאלה 6","VideoQuestionID":287,"VideoID":38721,"Type":"middle","TimeStampString":"00:00:01","TimeStamp":1,"OrderNumber":0,"VideoName":null,"Active":true,"VideoQuestionAnswersItems":[{"ID":1149,"Answer":"\u003cp\u003e\\({x^2} + 7x - 8 = \u0026nbsp;- 14\\)\u003c/p\u003e","Type":false},{"ID":1150,"Answer":"\u003cp\u003e\\({x_{1,2}} = \\frac{{ - 7 \\pm \\sqrt {{7^2} - 4 \\cdot 1 \\cdot \\left( { - 8} \\right)} }}{{2 \\cdot 1}}\\)\u003c/p\u003e","Type":false},{"ID":1151,"Answer":"\u003cp\u003e\\({x_{1,2}} = \\frac{{ - 7 \\pm \\sqrt {81} }}{2}\\)\u003c/p\u003e","Type":true},{"ID":1152,"Answer":"\u003cp\u003e\\({x_{1,2}} = \\frac{{ - 7 \\pm 9}}{2}\\)\u003c/p\u003e","Type":false},{"ID":1153,"Answer":"\u003cp\u003e\\({x_1} = \\frac{{ - 7 + 9}}{2}{\\rm{ = 1 \u0026nbsp;, \u0026nbsp;}}{x_2} = \\frac{{ - 7 - 9}}{2} = \u0026nbsp;- 8\\)\u003c/p\u003e","Type":false}],"TopicName":null,"CorrectAnswer":"\u003cp\u003e\\({x_{1,2}} = \\frac{{ - 7 \\pm \\sqrt {81} }}{2}\\)\u003c/p\u003e","Answer1":"\u003cp\u003e\\({x^2} + 7x - 8 = \u0026nbsp;- 14\\)\u003c/p\u003e","Answer2":"\u003cp\u003e\\({x_{1,2}} = \\frac{{ - 7 \\pm \\sqrt {{7^2} - 4 \\cdot 1 \\cdot \\left( { - 8} \\right)} }}{{2 \\cdot 1}}\\)\u003c/p\u003e","Answer3":"\u003cp\u003e\\({x_{1,2}} = \\frac{{ - 7 \\pm 9}}{2}\\)\u003c/p\u003e","Answer4":"\u003cp\u003e\\({x_1} = \\frac{{ - 7 + 9}}{2}{\\rm{ = 1 \u0026nbsp;, \u0026nbsp;}}{x_2} = \\frac{{ - 7 - 9}}{2} = \u0026nbsp;- 8\\)\u003c/p\u003e","Explanation":"\u003cp\u003eניתן להשתמש בנוסחת השורשים לפתור משוואה ריבועית רק כאשר אגף אחד במשוואה הוא (\\0)\\.\u003c/p\u003e","Question":"\u003cp\u003eיעל פתרה את המשוואה: \u0026nbsp;\\(x\\left( {x + 7} \\right) - 8 = \u0026nbsp;- 14\\) \u0026nbsp;באופן שגוי.\u003cbr\u003eבאיזו שורה נפלה טעות?\u003c/p\u003e"}],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[]],[[],[{"ID":201,"VideoQuestionName":"שאלה 1","VideoQuestionID":288,"VideoID":38745,"Type":"middle","TimeStampString":"00:00:00","TimeStamp":0,"OrderNumber":0,"VideoName":null,"Active":true,"VideoQuestionAnswersItems":[{"ID":1154,"Answer":"\u003cp\u003e\\({x^8} - 3{x^4} + 4 = 0\\)\u003c/p\u003e","Type":false},{"ID":1155,"Answer":"\u003cp\u003e\\({x^4} - 8{x^3} + 2 = 0\\)\u003c/p\u003e","Type":true},{"ID":1156,"Answer":"\u003cp\u003e\\({\\left( {1 + x} \\right)^4} - {\\left( {1 + x} \\right)^2} = 10\\)\u003c/p\u003e","Type":false},{"ID":1157,"Answer":"\u003cp\u003e\\(\\left( {{x^2} - 2x} \\right)\\left( {{x^2} - 2x + 3} \\right) = 4\\)\u003c/p\u003e","Type":false}],"TopicName":null,"CorrectAnswer":"\u003cp\u003e\\({x^4} - 8{x^3} + 2 = 0\\)\u003c/p\u003e","Answer1":"\u003cp\u003e\\({x^8} - 3{x^4} + 4 = 0\\)\u003c/p\u003e","Answer2":"\u003cp\u003e\\({\\left( {1 + x} \\right)^4} - {\\left( {1 + x} \\right)^2} = 10\\)\u003c/p\u003e","Answer3":"\u003cp\u003e\\(\\left( {{x^2} - 2x} \\right)\\left( {{x^2} - 2x + 3} \\right) = 4\\)\u003c/p\u003e","Answer4":null,"Explanation":"\u003cp\u003eמשוואה דו ריבועית היא משוואה שבה אותו הביטוי חוזר בשתי חזקות הגדולות פי שתיים אחת מהשנייה.\u003c/p\u003e","Question":"\u003cp\u003eאיזו משוואה אינה משוואה דו ריבועית?\u003c/p\u003e"},{"ID":202,"VideoQuestionName":"שאלה 2","VideoQuestionID":289,"VideoID":38745,"Type":"middle","TimeStampString":"00:00:00","TimeStamp":0,"OrderNumber":0,"VideoName":null,"Active":true,"VideoQuestionAnswersItems":[{"ID":1158,"Answer":"\u003cp\u003e\\(t = {x^2}\\)\u003c/p\u003e","Type":false},{"ID":1159,"Answer":"\u003cp\u003e\\(t = x\\)\u003c/p\u003e","Type":false},{"ID":1160,"Answer":"\u003cp\u003e\\(t = {x^2} - 3x + 4\\)\u003c/p\u003e","Type":false},{"ID":1161,"Answer":"\u003cp\u003e\\(t = {x^2} - 3x\\)\u003c/p\u003e","Type":true}],"TopicName":null,"CorrectAnswer":"\u003cp\u003e\\(t = {x^2} - 3x\\)\u003c/p\u003e","Answer1":"\u003cp\u003e\\(t = {x^2}\\)\u003c/p\u003e","Answer2":"\u003cp\u003e\\(t = x\\)\u003c/p\u003e","Answer3":"\u003cp\u003e\\(t = {x^2} - 3x + 4\\)\u003c/p\u003e","Answer4":null,"Explanation":"\u003cp\u003eהביטוי שנחליף בהצבה הוא הביטוי שכולל את הנעלם וחוזר על עצמו לאורך המשוואה וניתן להחליף בכדי שלא יישאר הנעלם.\u003c/p\u003e","Question":"\u003cp\u003eנתונה המשוואה: \u0026nbsp;\\(\\frac{{{x^2} - 3x}}{{{x^2} - 3x + 1}} + \\frac{2}{{{x^2} - 3x + 4}} = 3\\).\u003cbr\u003eאיזה ביטוי נסמן ב-t?\u003c/p\u003e"},{"ID":203,"VideoQuestionName":"שאלה 3","VideoQuestionID":290,"VideoID":38745,"Type":"middle","TimeStampString":"00:00:00","TimeStamp":0,"OrderNumber":0,"VideoName":null,"Active":true,"VideoQuestionAnswersItems":[{"ID":1162,"Answer":"\u003cp\u003e\\({x^2} - 2{x^3} + {x^4} = 3x - 3{x^2} + 4\\)\u003c/p\u003e","Type":false},{"ID":1163,"Answer":"\u003cp\u003eנסמן: \u0026nbsp;\\(t = {x^2}\\) ונקבל: \u0026nbsp;\\({\\left( {x - t} \\right)^2} = 3\\left( {x - t} \\right) + 4\\)\u003c/p\u003e","Type":false},{"ID":1164,"Answer":"\u003cp\u003eנסמן: \u0026nbsp;\\(t = x - {x^2}\\) ונקבל: \u0026nbsp;\\({t^2} = 3t + 4\\)\u003c/p\u003e","Type":true},{"ID":1165,"Answer":"\u003cp\u003e\\({\\left( { - x} \\right)^2} = 3 \\cdot \\left( { - x} \\right) + 4\\)\u003c/p\u003e","Type":false}],"TopicName":null,"CorrectAnswer":"\u003cp\u003eנסמן: \u0026nbsp;\\(t = x - {x^2}\\) ונקבל: \u0026nbsp;\\({t^2} = 3t + 4\\)\u003c/p\u003e","Answer1":"\u003cp\u003e\\({x^2} - 2{x^3} + {x^4} = 3x - 3{x^2} + 4\\)\u003c/p\u003e","Answer2":"\u003cp\u003eנסמן: \u0026nbsp;\\(t = {x^2}\\) ונקבל: \u0026nbsp;\\({\\left( {x - t} \\right)^2} = 3\\left( {x - t} \\right) + 4\\)\u003c/p\u003e","Answer3":"\u003cp\u003e\\({\\left( { - x} \\right)^2} = 3 \\cdot \\left( { - x} \\right) + 4\\)\u003c/p\u003e","Answer4":null,"Explanation":"\u003cp\u003eהביטוי שנחליף בהצבה הוא הביטוי שכולל את הנעלם וחוזר על עצמו לאורך המשוואה וניתן להחליף בכדי שלא יישאר הנעלם.\u003c/p\u003e","Question":"\u003cp\u003eמה השלב הבא בפתרון המשוואה: \u0026nbsp;\\({\\left( {x - {x^2}} \\right)^2} = 3\\left( {x - {x^2}} \\right) + 4\\)?\u003c/p\u003e"},{"ID":204,"VideoQuestionName":"שאלה 4","VideoQuestionID":291,"VideoID":38745,"Type":"middle","TimeStampString":"00:00:00","TimeStamp":0,"OrderNumber":0,"VideoName":null,"Active":true,"VideoQuestionAnswersItems":[{"ID":1166,"Answer":"\u003cp\u003eנסמן: \u0026nbsp;\\(t = {x^2}\\)\u003c/p\u003e","Type":false},{"ID":1167,"Answer":"\u003cp\u003e\\({t^2} + 4t = 0\\)\u003c/p\u003e","Type":false},{"ID":1168,"Answer":"\u003cp\u003e\\(t\\left( {t + 4} \\right) = 0\\)\u003c/p\u003e","Type":false},{"ID":1169,"Answer":"\u003cp\u003e\\(t = 0{\\rm{ }},\\;t = \u0026nbsp;- 4\\)\u003c/p\u003e","Type":false},{"ID":1170,"Answer":"\u003cp\u003e\\(x = 0{\\rm{ }},\\;x = \u0026nbsp;- 4\\)\u003c/p\u003e","Type":true}],"TopicName":null,"CorrectAnswer":"\u003cp\u003e\\(x = 0{\\rm{ }},\\;x = \u0026nbsp;- 4\\)\u003c/p\u003e","Answer1":"\u003cp\u003eנסמן: \u0026nbsp;\\(t = {x^2}\\)\u003c/p\u003e","Answer2":"\u003cp\u003e\\({t^2} + 4t = 0\\)\u003c/p\u003e","Answer3":"\u003cp\u003e\\(t\\left( {t + 4} \\right) = 0\\)\u003c/p\u003e","Answer4":"\u003cp\u003e\\(t = 0{\\rm{ }},\\;t = \u0026nbsp;- 4\\)\u003c/p\u003e","Explanation":"\u003cp\u003eצריך להשוות את ערך הנעלם המוצב לביטוי אותו הוא מחליף ואז לגלות את ערכי הנעלם המקורי.\u003c/p\u003e","Question":"\u003cp\u003eזיו טעה בפתרון המשוואה: \u0026nbsp;\\({x^4} + 4{x^2} = 0\\).\u003cbr\u003eסמנו באיזו שורה נפלה הטעות.\u003c/p\u003e"}],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[]],[[{"ID":205,"VideoQuestionName":"שאלה 1","VideoQuestionID":292,"VideoID":38782,"Type":"middle","TimeStampString":"00:00:01","TimeStamp":1,"OrderNumber":0,"VideoName":null,"Active":true,"VideoQuestionAnswersItems":[{"ID":1171,"Answer":"\u003cp\u003e\\(x = \\frac{1}{m}\\)\u003c/p\u003e","Type":true},{"ID":1172,"Answer":"\u003cp\u003e\\(m = \\frac{1}{x}\\)\u003c/p\u003e","Type":false},{"ID":1173,"Answer":"\u003cp\u003e\\(x = 1\\)\u003c/p\u003e","Type":false},{"ID":1174,"Answer":"\u003cp\u003e\\(x = \\frac{m}{1}\\)\u003c/p\u003e","Type":false}],"TopicName":null,"CorrectAnswer":"\u003cp\u003e\\(x = \\frac{1}{m}\\)\u003c/p\u003e","Answer1":"\u003cp\u003e\\(m = \\frac{1}{x}\\)\u003c/p\u003e","Answer2":"\u003cp\u003e\\(x = 1\\)\u003c/p\u003e","Answer3":"\u003cp\u003e\\(x = \\frac{m}{1}\\)\u003c/p\u003e","Answer4":null,"Explanation":"\u003cp\u003eבפתרון משוואה נבודד את הנעלם על מנת לגלות את ערך הנעלם שהצבתו במשוואה תניב פסוק אמת.\u003c/p\u003e","Question":"\u003cp\u003eמה הפתרון של המשוואה הבאה: \u0026nbsp;\\(mx = 1\\)?\u003c/p\u003e"},{"ID":206,"VideoQuestionName":"שאלה 2","VideoQuestionID":293,"VideoID":38782,"Type":"middle","TimeStampString":"00:00:01","TimeStamp":1,"OrderNumber":0,"VideoName":null,"Active":true,"VideoQuestionAnswersItems":[{"ID":1175,"Answer":"\u003cp\u003e\\(2x + 3 = mx - m\\)\u003c/p\u003e","Type":false},{"ID":1176,"Answer":"\u003cp\u003e\\(2x + m - mx + 3 = 0\\)\u003c/p\u003e","Type":false},{"ID":1177,"Answer":"\u003cp\u003e\\(2x - mx = \u0026nbsp;- m - 3\\)\u003c/p\u003e","Type":true},{"ID":1178,"Answer":"\u003cp\u003e\\(2x + m - mx = \u0026nbsp;- 3\\)\u003c/p\u003e","Type":false}],"TopicName":null,"CorrectAnswer":"\u003cp\u003e\\(2x - mx = \u0026nbsp;- m - 3\\)\u003c/p\u003e","Answer1":"\u003cp\u003e\\(2x + 3 = mx - m\\)\u003c/p\u003e","Answer2":"\u003cp\u003e\\(2x + m - mx + 3 = 0\\)\u003c/p\u003e","Answer3":"\u003cp\u003e\\(2x + m - mx = \u0026nbsp;- 3\\)\u003c/p\u003e","Answer4":null,"Explanation":"\u003cp\u003eבפתרון משוואה נבודד את הנעלם על מנת לגלות את ערך הנעלם שהצבתו במשוואה תניב פסוק אמת.\u003c/p\u003e","Question":"\u003cp\u003eמה השלב הבא בפתרון המשוואה: \u0026nbsp;\\(2x + m = mx - 3\\)?\u003c/p\u003e"},{"ID":207,"VideoQuestionName":"שאלה 3","VideoQuestionID":294,"VideoID":38782,"Type":"middle","TimeStampString":"00:00:01","TimeStamp":1,"OrderNumber":0,"VideoName":null,"Active":true,"VideoQuestionAnswersItems":[{"ID":1179,"Answer":"\u003cp\u003e\\({x_{1,2}} = \\frac{{ - \\left( {m + 1} \\right) \\pm \\sqrt {{{\\left( {m + 1} \\right)}^2} - 4m\\left( { - m + 1} \\right)} }}{{2m}}\\)\u003c/p\u003e","Type":false},{"ID":1180,"Answer":"\u003cp\u003e\\({x_{1,2}} = \\frac{{ - \\left( { - \\left( {m + 1} \\right)} \\right) \\pm \\sqrt {{{\\left( { - \\left( {m + 1} \\right)} \\right)}^2} - 4m\\left( { - m + 1} \\right)} }}{{2m}}\\)\u003c/p\u003e","Type":true},{"ID":1181,"Answer":"\u003cp\u003e\\({x_{1,2}} = \\frac{{m + 1 \\pm \\sqrt {{{\\left( {m + 1} \\right)}^2} - 4m\\left( {m + 1} \\right)} }}{{2m}}\\)\u003c/p\u003e","Type":false},{"ID":1182,"Answer":"\u003cp\u003e\\({x_{1,2}} = \\frac{{ - \\left( {m + 1} \\right) \\pm \\sqrt {{{\\left( {m + 1} \\right)}^2} - 4m\\left( {m + 1} \\right)} }}{{2m}}\\)\u003c/p\u003e","Type":false}],"TopicName":null,"CorrectAnswer":"\u003cp\u003e\\({x_{1,2}} = \\frac{{ - \\left( { - \\left( {m + 1} \\right)} \\right) \\pm \\sqrt {{{\\left( { - \\left( {m + 1} \\right)} \\right)}^2} - 4m\\left( { - m + 1} \\right)} }}{{2m}}\\)\u003c/p\u003e","Answer1":"\u003cp\u003e\\({x_{1,2}} = \\frac{{ - \\left( {m + 1} \\right) \\pm \\sqrt {{{\\left( {m + 1} \\right)}^2} - 4m\\left( { - m + 1} \\right)} }}{{2m}}\\)\u003c/p\u003e","Answer2":"\u003cp\u003e\\({x_{1,2}} = \\frac{{m + 1 \\pm \\sqrt {{{\\left( {m + 1} \\right)}^2} - 4m\\left( {m + 1} \\right)} }}{{2m}}\\)\u003c/p\u003e","Answer3":"\u003cp\u003e\\({x_{1,2}} = \\frac{{ - \\left( {m + 1} \\right) \\pm \\sqrt {{{\\left( {m + 1} \\right)}^2} - 4m\\left( {m + 1} \\right)} }}{{2m}}\\)\u003c/p\u003e","Answer4":null,"Explanation":"\u003cp\u003eבמשוואה ריבועית (\\a)\\ הוא מקדם של הנעלם בריבוע.\u003cbr\u003e(\\b)\\ הוא המקדם של הנעלם במעלה ראשונה. (\\c)\\ הוא האיבר החופשי.\u003cbr\u003eנוסחת השורשים היא: \u0026nbsp;\\(x = \\frac{{ - b \\pm \\sqrt {{{\\left( b \\right)}^2} - 4ac} }}{{2a}}\\)\u003c/p\u003e","Question":"\u003cp\u003eנתונה המשוואה: \u0026nbsp;\\(m{x^2} - \\left( {m + 1} \\right)x - m + 1 = 0\\).\u003cbr\u003eאיך נציב אותה בנוסחת השורשים?\u003c/p\u003e"},{"ID":208,"VideoQuestionName":"שאלה 4","VideoQuestionID":295,"VideoID":38782,"Type":"middle","TimeStampString":"00:00:01","TimeStamp":1,"OrderNumber":0,"VideoName":null,"Active":true,"VideoQuestionAnswersItems":[{"ID":1183,"Answer":"\u003cp\u003eנכפול את המשוואה הראשונה ב-\\(\\left( {m + 1} \\right)\\).\u003c/p\u003e","Type":false},{"ID":1184,"Answer":"\u003cp\u003eנבודד את y מהמשוואה הראשונה.\u003c/p\u003e","Type":false},{"ID":1185,"Answer":"\u003cp\u003eנכפול את המשוואה השנייה ב-\\( - \\left( {m - 2} \\right)\\).\u003c/p\u003e","Type":false},{"ID":1186,"Answer":"\u003cp\u003eנפתח סוגריים בשתי המשוואות.\u003c/p\u003e","Type":true}],"TopicName":null,"CorrectAnswer":"\u003cp\u003eנפתח סוגריים בשתי המשוואות.\u003c/p\u003e","Answer1":"\u003cp\u003eנכפול את המשוואה הראשונה ב-\\(\\left( {m + 1} \\right)\\).\u003c/p\u003e","Answer2":"\u003cp\u003eנבודד את y מהמשוואה הראשונה.\u003c/p\u003e","Answer3":"\u003cp\u003eנכפול את המשוואה השנייה ב-\\( - \\left( {m - 2} \\right)\\).\u003c/p\u003e","Answer4":null,"Explanation":"\u003cp\u003eבשיטת השוואת מקדמים נרצה לצמצם נעלם בעל מקדם מספרי דומה בשתי המשוואות על ידי חיבור או חיסור.\u003cbr\u003eבשיטת ההצבה נרצה לבודד ביטוי במשוואה אחת כדי להציב אותו בשנייה ובכך לצמצם את כמות הנעלמים.\u003c/p\u003e","Question":"\u003cp\u003eמה לא יכול \u0026nbsp;להיות שלב הבא בפתרון המערכת: \u0026nbsp;\\(\\begin{array}{l}\\left( {m - 2} \\right)x + y = 1\\\\x + \\left( {m + 1} \\right)y = 3\\end{array}\\).\u003c/p\u003e"}],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[]],[[{"ID":209,"VideoQuestionName":"שאלה 1","VideoQuestionID":296,"VideoID":38800,"Type":"middle","TimeStampString":"00:00:01","TimeStamp":1,"OrderNumber":0,"VideoName":null,"Active":true,"VideoQuestionAnswersItems":[{"ID":1187,"Answer":"\u003cp\u003e\\(x = \u0026nbsp;- 1\\)\u003c/p\u003e","Type":false},{"ID":1188,"Answer":"\u003cp\u003e\\(x = \u0026nbsp;- 2\\)\u003c/p\u003e","Type":false},{"ID":1189,"Answer":"\u003cp\u003e\\(x = 4\\)\u003c/p\u003e","Type":true},{"ID":1190,"Answer":"\u003cp\u003e\\(x = 0\\)\u003c/p\u003e","Type":false}],"TopicName":null,"CorrectAnswer":"\u003cp\u003e\\(x = 4\\)\u003c/p\u003e","Answer1":"\u003cp\u003e\\(x = \u0026nbsp;- 1\\)\u003c/p\u003e","Answer2":"\u003cp\u003e\\(x = \u0026nbsp;- 2\\)\u003c/p\u003e","Answer3":"\u003cp\u003e\\(x = 0\\)\u003c/p\u003e","Answer4":null,"Explanation":"\u003cp\u003eפתרון משוואה הוא ערך של הנעלם אשר הצבתו במשוואה מניבה פסוק אמת.\u003c/p\u003e","Question":"\u003cp\u003eמה הפתרון של המשוואה: \u0026nbsp;\\(\\sqrt {3x + 4} \u0026nbsp;= x\\)?\u003c/p\u003e"},{"ID":210,"VideoQuestionName":"שאלה 2","VideoQuestionID":297,"VideoID":38800,"Type":"middle","TimeStampString":"00:00:01","TimeStamp":1,"OrderNumber":0,"VideoName":null,"Active":true,"VideoQuestionAnswersItems":[{"ID":1191,"Answer":"\u003cp\u003e\\(x + 4 = {x^2} + 9\\)\u003c/p\u003e","Type":false},{"ID":1192,"Answer":"\u003cp\u003e\\(x + 4 = {\\left( {x + 3} \\right)^2}\\)\u003c/p\u003e","Type":true},{"ID":1193,"Answer":"\u003cp\u003e\\({\\left( {x + 4} \\right)^2} = {\\left( {x + 3} \\right)^2}\\)\u003c/p\u003e","Type":false},{"ID":1194,"Answer":"\u003cp\u003e\\({\\left( {x + 4} \\right)^2} = x + 3\\)\u003c/p\u003e","Type":false}],"TopicName":null,"CorrectAnswer":"\u003cp\u003e\\(x + 4 = {\\left( {x + 3} \\right)^2}\\)\u003c/p\u003e","Answer1":"\u003cp\u003e\\(x + 4 = {x^2} + 9\\)\u003c/p\u003e","Answer2":"\u003cp\u003e\\({\\left( {x + 4} \\right)^2} = {\\left( {x + 3} \\right)^2}\\)\u003c/p\u003e","Answer3":"\u003cp\u003e\\({\\left( {x + 4} \\right)^2} = x + 3\\)\u003c/p\u003e","Answer4":null,"Explanation":"\u003cp\u003eבפתרון משוואה עם שורשים, נבודד שורש באגף של המשוואה ונעלה את 2 אגפי המשוואה במלואם בריבוע.\u003c/p\u003e","Question":"\u003cp\u003eמה השלב הבא בפתרון המשוואה: \u0026nbsp;\\(\\sqrt {x + 4} \u0026nbsp;= x + 3\\)?\u003c/p\u003e"},{"ID":211,"VideoQuestionName":"שאלה 3","VideoQuestionID":298,"VideoID":38800,"Type":"middle","TimeStampString":"00:00:01","TimeStamp":1,"OrderNumber":0,"VideoName":null,"Active":true,"VideoQuestionAnswersItems":[{"ID":1195,"Answer":"\u003cp\u003e\\(\\sqrt {3 - x} \u0026nbsp;= 3 - \\sqrt {x + 2} \\)\u003c/p\u003e","Type":false},{"ID":1196,"Answer":"\u003cp\u003e\\({\\left( {\\sqrt {3 - x} \u0026nbsp;+ \\sqrt {x + 2} } \\right)^2} = 9\\)\u003c/p\u003e","Type":false},{"ID":1197,"Answer":"\u003cp\u003e\\(\\sqrt {x + 2} \u0026nbsp;= 3 - \\sqrt {3 - x} \\)\u003c/p\u003e","Type":false},{"ID":1198,"Answer":"\u003cp\u003e\\(\\sqrt {3 - x + x + 2} \u0026nbsp;= 3\\)\u003c/p\u003e","Type":true}],"TopicName":null,"CorrectAnswer":"\u003cp\u003e\\(\\sqrt {3 - x + x + 2} \u0026nbsp;= 3\\)\u003c/p\u003e","Answer1":"\u003cp\u003e\\(\\sqrt {3 - x} \u0026nbsp;= 3 - \\sqrt {x + 2} \\)\u003c/p\u003e","Answer2":"\u003cp\u003e\\({\\left( {\\sqrt {3 - x} \u0026nbsp;+ \\sqrt {x + 2} } \\right)^2} = 9\\)\u003c/p\u003e","Answer3":"\u003cp\u003e\\(\\sqrt {x + 2} \u0026nbsp;= 3 - \\sqrt {3 - x} \\)\u003c/p\u003e","Answer4":null,"Explanation":"\u003cp\u003eלא ניתן לחבר או לחסר שורשים נפרדים תחת שורש יחיד.\u003c/p\u003e","Question":"\u003cp\u003eמה לא יכול להיות השלב הבא בפתרון המשוואה: \u0026nbsp;\\(\\sqrt {3 - x} \u0026nbsp;+ \\sqrt {x + 2} \u0026nbsp;= 3\\)?\u003c/p\u003e"},{"ID":212,"VideoQuestionName":"שאלה 4","VideoQuestionID":299,"VideoID":38800,"Type":"middle","TimeStampString":"00:00:01","TimeStamp":1,"OrderNumber":0,"VideoName":null,"Active":true,"VideoQuestionAnswersItems":[{"ID":1199,"Answer":"\u003cp\u003e\\(x\\sqrt x \u0026nbsp;= 8\\)\u003c/p\u003e","Type":false},{"ID":1200,"Answer":"\u003cp\u003e\\(x \\cdot x = 64\\)\u003c/p\u003e","Type":true},{"ID":1201,"Answer":"\u003cp\u003e\\({x^2} = 64\\)\u003c/p\u003e","Type":false},{"ID":1202,"Answer":"\u003cp\u003e\\(x = 8{\\rm{ }},\\;x = \u0026nbsp;- 8\\)\u003c/p\u003e","Type":false}],"TopicName":null,"CorrectAnswer":"\u003cp\u003e\\(x \\cdot x = 64\\)\u003c/p\u003e","Answer1":"\u003cp\u003e\\(x\\sqrt x \u0026nbsp;= 8\\)\u003c/p\u003e","Answer2":"\u003cp\u003e\\({x^2} = 64\\)\u003c/p\u003e","Answer3":"\u003cp\u003e\\(x = 8{\\rm{ }},\\;x = \u0026nbsp;- 8\\)\u003c/p\u003e","Answer4":null,"Explanation":"\u003cp\u003eהעלאה בריבוע של מכפלה מעלה כל גורם במכפלה בנפרד בריבוע.\u003c/p\u003e","Question":"\u003cp\u003eנפלה טעות בפתרון של נעם למשוואה: \u0026nbsp;\\(x\\sqrt x \u0026nbsp;- 8 = 0\\).\u003cbr\u003eסמנו באיזו שורה נפלה הטעות.\u003c/p\u003e"}],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[]],[[{"ID":216,"VideoQuestionName":"שאלה 1","VideoQuestionID":303,"VideoID":38638,"Type":"middle","TimeStampString":"00:00:01","TimeStamp":1,"OrderNumber":0,"VideoName":null,"Active":true,"VideoQuestionAnswersItems":[{"ID":1215,"Answer":"\u003cp\u003e\\(\\begin{array}{l}{x^2} + {y^2} = 25\\\\{x^2} + {y^2} = 49\\end{array}\\)\u003c/p\u003e","Type":false},{"ID":1216,"Answer":"\u003cp\u003e\\(\\begin{array}{l}{x^2} + {y^2} = 25\\\\y = x - 7\\end{array}\\)\u003c/p\u003e","Type":false},{"ID":1217,"Answer":"\u003cp\u003e\\(\\begin{array}{l}{x^2} + {y^2} = 25\\\\x = 7 - y\\end{array}\\)\u003c/p\u003e","Type":true},{"ID":1218,"Answer":"\u003cp\u003e\\(\\begin{array}{l}x + y = 5\\\\x + y = 7\\end{array}\\)\u003c/p\u003e","Type":false}],"TopicName":null,"CorrectAnswer":"\u003cp\u003e\\(\\begin{array}{l}{x^2} + {y^2} = 25\\\\x = 7 - y\\end{array}\\)\u003c/p\u003e","Answer1":"\u003cp\u003e\\(\\begin{array}{l}{x^2} + {y^2} = 25\\\\{x^2} + {y^2} = 49\\end{array}\\)\u003c/p\u003e","Answer2":"\u003cp\u003e\\(\\begin{array}{l}{x^2} + {y^2} = 25\\\\y = x - 7\\end{array}\\)\u003c/p\u003e","Answer3":"\u003cp\u003e\\(\\begin{array}{l}x + y = 5\\\\x + y = 7\\end{array}\\)\u003c/p\u003e","Answer4":null,"Explanation":"\u003cp\u003eעל מנת לפתור מערכת משוואות שבה לא ניתן להשוות מקדמים מאחר והנעלמים בחזקות שונות בין המשוואות,\u003cbr\u003eנשתמש בשיטת ההצבה. נבודד נעלם אחד במשוואה אחת ונציב במשוואה השנייה.\u003c/p\u003e","Question":"\u003cp\u003eמה השלב הבא בפתרון המערכת: \\(\\begin{array}{l}{x^2} + {y^2} = 25\\\\x + y = 7\\end{array}\\) ?\u003c/p\u003e"},{"ID":217,"VideoQuestionName":"שאלה 2","VideoQuestionID":304,"VideoID":38638,"Type":"middle","TimeStampString":"00:00:01","TimeStamp":1,"OrderNumber":0,"VideoName":null,"Active":true,"VideoQuestionAnswersItems":[{"ID":1219,"Answer":"\u003cp\u003e\\({\\left( {\\frac{{20}}{y}} \\right)^2} - 4{y^2} = 34\\)\u003c/p\u003e","Type":false},{"ID":1220,"Answer":"\u003cp\u003e\\(2 \\cdot {\\frac{{10}}{y}^2} - 4{y^2} = 34\\)\u003c/p\u003e","Type":false},{"ID":1221,"Answer":"\u003cp\u003e\\(\\frac{{20}}{{{y^2}}} - 4{y^2} = 34\\)\u003c/p\u003e","Type":false},{"ID":1222,"Answer":"\u003cp\u003e\\(2 \\cdot {\\left( {\\frac{{10}}{y}} \\right)^2} - 4{y^2} = 34\\)\u003c/p\u003e","Type":true}],"TopicName":null,"CorrectAnswer":"\u003cp\u003e\\(2 \\cdot {\\left( {\\frac{{10}}{y}} \\right)^2} - 4{y^2} = 34\\)\u003c/p\u003e","Answer1":"\u003cp\u003e\\({\\left( {\\frac{{20}}{y}} \\right)^2} - 4{y^2} = 34\\)\u003c/p\u003e","Answer2":"\u003cp\u003e\\(2 \\cdot {\\frac{{10}}{y}^2} - 4{y^2} = 34\\)\u003c/p\u003e","Answer3":"\u003cp\u003e\\(\\frac{{20}}{{{y^2}}} - 4{y^2} = 34\\)\u003c/p\u003e","Answer4":null,"Explanation":"\u003cp\u003eבשיטת ההצבה תמיד נחליף את הנעלם המוצב בביטוי השקול לו, בסוגריים.\u003c/p\u003e","Question":"\u003cp\u003eנתונה מערכת משוואות: \u0026nbsp;\\(\\begin{array}{l}2{x^2} - 4{y^2} = 34\\\\x = \\frac{{10}}{y}\\end{array}\\).\u003cbr\u003eאיך נציב את המשוואה השנייה במשוואה הראשונה?\u003c/p\u003e"},{"ID":218,"VideoQuestionName":"שאלה 3","VideoQuestionID":305,"VideoID":38638,"Type":"middle","TimeStampString":"00:00:01","TimeStamp":1,"OrderNumber":0,"VideoName":null,"Active":true,"VideoQuestionAnswersItems":[{"ID":1223,"Answer":"\u003cp\u003eנבודד את x מהמשוואה הראשונה: \u0026nbsp;\\(\\frac{{{x^2} + {y^2}}}{y} = x\\).\u003c/p\u003e","Type":false},{"ID":1224,"Answer":"\u003cp\u003eנשווה את 2 האגפים הימניים: \u0026nbsp;\\(xy = 4 - xy\\).\u003c/p\u003e","Type":true},{"ID":1225,"Answer":"\u003cp\u003eנבודד את y מהמשוואה הראשונה בעזרת הוצאת שורש: \u0026nbsp;\\(y = \\sqrt {xy - {x^2}} \\).\u003c/p\u003e","Type":false},{"ID":1226,"Answer":"\u003cp\u003eנבודד את \\({x^2}\\) מהמשוואה השנייה: \u0026nbsp;\\({x^2} = 4 - xy - {y^2}\\).\u003c/p\u003e","Type":false}],"TopicName":null,"CorrectAnswer":"\u003cp\u003eנשווה את 2 האגפים הימניים: \u0026nbsp;\\(xy = 4 - xy\\).\u003c/p\u003e","Answer1":"\u003cp\u003eנבודד את x מהמשוואה הראשונה: \u0026nbsp;\\(\\frac{{{x^2} + {y^2}}}{y} = x\\).\u003c/p\u003e","Answer2":"\u003cp\u003eנבודד את y מהמשוואה הראשונה בעזרת הוצאת שורש: \u0026nbsp;\\(y = \\sqrt {xy - {x^2}} \\).\u003c/p\u003e","Answer3":"\u003cp\u003eנבודד את \\({x^2}\\) מהמשוואה השנייה: \u0026nbsp;\\({x^2} = 4 - xy - {y^2}\\).\u003c/p\u003e","Answer4":null,"Explanation":"\u003cp\u003eבשיטת ההצבה, ניתן להחליף ביטוי בביטוי שקול לו ממשוואה אחת לאחרת.\u003c/p\u003e","Question":"\u003cp\u003eמה השלב הבא בפתרון המשוואה: \u0026nbsp;\\(\\begin{array}{l}{x^2} + {y^2} = xy\\\\{x^2} + {y^2} = 4 - xy\\end{array}\\)?\u003c/p\u003e"}],[],[],[],[],[],[],[],[],[],[],[],[],[],[]]]