Question

$8x - 12 leqslant 2 {x}^{2} - 2x$
Кто сможет

Answer 1

$8x-12 leq 2 x^{2} -2x$
$8x-12-2 x^{2} -2x leq 0$
$10x-12-2x^{2} leq 0$
$5x-6-x^{2} leq 0$
$- x^{2} +5x-6 leq 0$
$- x^{2} +3x+2x-6 leq 0$
$-x(x-3)+2(x-3) leq 0$
$(-x+2)(x-3) leq 0$
рассматриваем два случая:
$1) left { {-x+2 leq 0} atop {x-3 geq 0}} right. left { {{x geq 2} atop {x geq 3}} right.$
$2) left { {{-x+2 geq 0} atop {x-3 leq 0}} right. left { {{x leq 2} atop {x leq 3}} right.$
1) x∈[3,+∞)
2) x∈(-∞,2]
ответ: x∈(-∞,2]∪[3,+∞)