Question

Кто-нибудь знает как решить это с пояснением?
(всего 18 баллов, больше нет просто)

Answer 1

$\displaystyle\bf\\\frac{2(x-1)^{2} -3|x-1|+3}{(x-1)^{2} +1} \geq 1\\\\\\(x-1)^{2} =|x-1|^{2} \\\\|x-1|=m \ , \ m\geq 0\\\\\\\frac{2m^{2}-3m+3 }{m^{2} +1}-1\geq 0\\\\\\\frac{2m^{2} -3m+3-m^{2} -1}{m^{2} +1} \geq 0\\\\\\\frac{m^{2} -3m+2}{m^{2} +1} \geq 0\\\\\\\frac{(m-1)(m-2)}{m^{2} +1} \geq 0\\\\\\m^{2} +1>0 \ \ ; \ \ m^{2} +1\neq 0\\\\(m-1)(m-2)\geq 0\\\\m\in(-\infty \ ; \ 1] \cup \ [2 \ ; \ +\infty)\\\\\\1) \ 0\leq |x-1|\leq 1\\\\-1\leq x-1\leq 1\\\\x\in[0 \ ; \ 2]$

$\displaystyle\bf\\2) \ |x-1|\geq 2\\\\x-1\leq -2\\\\x\leq -1\\\\\\x-1\geq 2\\\\x\geq 3\\\\x\in(-\infty \ ; \ -1] \ \cup \ [3 \ ; \ +\infty)$