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
$x_{1} = frac{7+17}{10}=2,4\\ x_{2}= frac{7-17}{10}=-1\\5(x-2,4)(x+1) geq 0\\(x-2,4)(x+1) geq 0$

       +                     -                        +
________________________________
              - 1                         2, 4

Ответ : x ∈ (- ∞ ; - 1] ∪ [2,4 ; + ∞)