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Консультация № 193393
15.06.2018, 23:23
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Здравствуйте! Прошу помощи в следующем вопросе: Решить неравенство
квадратный корень(-x^2+6x-5)>8-2x. Заранее благодарен.
квадратный корень(-x^2+6x-5)>8-2x. Заранее благодарен.
Обсуждение
15.06.2018, 23:38
общий
это ответ
Здравствуйте, Тимофеев Алексей Валентинович!
Если 8-2x<0 (x>4), то неравенство выполняется для всех допустимых х:
-x^2+6x-5>=0;
x^2-6x+5<=0,
1<=x<=5
4<x<= 5.
Если 8-2x>=0 (x<=4), то можно возвести в квадрат обе части неравенства:
-x^2+6x-5>4x^2-32x+64
5x^2-38x+69<0
3<x<4.6
Т.к. есть ограничения: 3<x<=4
Объединив решения: 3<x<=5
Если 8-2x<0 (x>4), то неравенство выполняется для всех допустимых х:
-x^2+6x-5>=0;
x^2-6x+5<=0,
1<=x<=5
4<x<= 5.
Если 8-2x>=0 (x<=4), то можно возвести в квадрат обе части неравенства:
-x^2+6x-5>4x^2-32x+64
5x^2-38x+69<0
3<x<4.6
Т.к. есть ограничения: 3<x<=4
Объединив решения: 3<x<=5
5
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