Решите неравенство: -2х²+5x-2 (больше либо равно) 0

Решите неравенство: -2х²+5x-2 (больше либо равно) 0
- Предмет:
  Математика
- Автор:
  sunnymhzq
- 6 лет назад

Ответы 1

$- 2 {x}^{2} + 5x - 2 \geqslant 0 \\ d = 25 - 4 \times ( - 2) \times ( - 2) = 25 - 16 = 9 \\ x1 = \frac{ - 5 + \sqrt{9} }{ - 4} = \frac{ - 5 + 3}{ - 4} = \frac{ - 2}{ - 4} = \frac{1}{2} = 0.5 \\ x2 = \frac{ - 5 - 3}{ - 4} = \frac{ - 8}{ - 4} = 2$ вспомним формулу и разложим на мгожители: $a {x}^{2} + bx + c = a(x - x1)(x - x2)$ $- 2(x - 0.5)(x - 2) \geqslant 0 \\ 0 \geqslant x - 0.5 \geqslant 0 \\ 0.5 \geqslant x \geqslant 0.5 \\ \\ 0 \geqslant x - 2 \geqslant 0 \\ 2 \geqslant x \geqslant 2 \\$ Найдем объединение и получим:х ∈ [0,5; 2]
- Автор:
  bruiser71
- 6 лет назад
- 0
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Решите неравенство: -2х²+5x-2 (больше либо равно) 0

Ответы 1

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