Question

Найти решение неравенства 5х^2-7x >= 12

Answer 1

5x² - 7x ≥ 12
5x² - 7x - 12 = 0
D = (- 7)² - 4 * 5 * (- 12) = 49 + 240 = 289 = 17²
$x_{1} = \frac{7+17}{10}=2,4\\\\ x_{2}= \frac{7-17}{10}=-1\\\\5(x-2,4)(x+1) \geq 0\\\\(x-2,4)(x+1) \geq 0$

       +                     -                        +
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              - 1                         2, 4

Ответ : x ∈ (- ∞ ; - 1] ∪ [2,4 ; + ∞)