Question

Решить неравенство $0,5 ^{x ^{2}-2 } geq frac{1}{4}$

Answer 1

$0,5^{x^2-2} geq frac{1}{4} \\0,5=frac{5}{10}=frac{1}{2}=2^{-1}; ,; ; frac{1}{4}=frac{1}{2^2}=2^{-2}\\\(2^{-1})^{x^2-2} geq 2^{-2}\\2^{-x^2+2} geq 2^{-2}\\-x^2+2 geq -2\\x^2-4 leq 0\\(x-2)(x+2) leq 0\\+++(-2)---(2)+++\\xin [, -2,2, ]$