Question

ДАМ 60 БАЛЛОВ!!!!
Решите систему неравенств.Система на фото в закрепе

Развёрнутый ответ

Answer 1

$\displaystyle\bf\\\left \{ {{2x - 7 \leqslant 0} \atop { - 2 {x}^{2} - 7x + 9 < 0 }} \right. \\ \\ - 2 {x}^{2} - 7x + 9 < 0 \\ 2 {x}^{2} + 7x - 9 > 0 \\ 2 {x}^{2} + 7x - 9 = 0 \\ a =2 \\ b = 7\\ c = - 9\\ D = {b}^{2} - 4ac = {7}^{2} - 4 \times 2 \times ( - 9) = \\ = 49 + 72 = 121 \\ x_{1} = \frac{ - 7 - 11}{2 \times 2} = - \frac{18}{4} = - 4.5 \\ x_{2} = \frac{ - 7 + 11}{2 \times 2} = \frac{4}{4} = 1 \\ (x + 4.5)(x - 1) > 0 \\ + + + ( - 4.5) - - - (1) + + + \\ x \: \epsilon\: ( - \propto; \: - 4.5)U( 1; \: + \propto) \\ \\ 2x - 7 \leqslant 0 \\ 2x \leqslant 7 \\ x \leqslant 3.5 \\ x \: \epsilon \: ( - \propto; \:3 .5] \\ \\ \displaystyle\bf\\\left \{ {{ x \: \epsilon \: ( - \propto; \: 3.5] } \atop { x \: \epsilon\: ( - \propto; \: - 4.5)U( 1; \: + \propto)}} \right. \\ \\ otvet \: \: \: x \: \epsilon\: ( - \propto; \: - 4.5)U(1; \: 3.5]$