Question

СРОЧНО !!сколько целых чисел удовлетворяют неравенству?

Answer 1

$x^2-8x+7 \leq 0\\\\t=x^2,\; t^2-8t+7 \leq 0\\\\t_1=1,\; t_2=7\; (teor.\; Vieta)\\\\+++[1]---[7]+++\\\\ \left \{ {{t \geq 1} \atop {t \leq 7}} \right. \\\\x^2 \geq 1\; \to \; x^2-1 \geq 0,\; \; (x-1)(x+1) \geq 0\\\\ +++[-1]---[1]+++\\\\x\in (-\infty,-1]U[1,+\infty)$

$\\x^2 \leq 7\; \; \to \; \; x^2-7 \leq 0,\; \; (x-\sqrt7)(x+\sqrt7) \leq 0\\\\+++[-\sqrt7]---[\sqrt7]+++\\\\x\in [-\sqrt7,\sqrt7]\\\\\\ \left \{ {{x\in (-\infty,-1]U[1,+\infty)} \atop {x\in [-\sqrt7,\sqrt7]}} \right. \; \; \to \; \; x\in [-\sqrt7,-1]U[1,\sqrt7]\\\\Celue:\; x=-2,-1,1,2.$