Решить неравенство [tex]0,5 ^{x ^{2}-2 } \geq \frac{1}{4} [/tex]. Created by CzarRWR. algebra-ru

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Решить неравенство [tex]0,5 ^{x ^{2}-2 } \geq \frac{1}{4} [/tex]

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

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