Question

(1/2)^x-1/x+2 больше равно 4 пж помогите

Answer 1

$\displaystyle\bf\\\Big(\frac{1}{2} \Big)^{\frac{x-1}{x+2} } \geq 4\\\\\\\Big(2^{-1} \Big)^{\frac{x-1}{x+2} } \geq 2^{2} \\\\\\2^{\frac{1-x}{x+2} } \geq 2^{2} \\\\\\2>1 \ \ \Rightarrow \ \ \frac{1-x}{x+2} \geq 2\\\\\\ \frac{1-x}{x+2} -2\geq 0\\\\\\\frac{1-x-2x-4}{x+2} \geq 0\\\\\\\frac{-3x-3}{x+2} \geq 0 \\\\\\\frac{-3(x+1)}{x+2} \geq0\\\\\\\frac{x+1}{x+2} \leq 0 \ \ ; \ x\neq -2$

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$\displaystyle\bf\\Otvet:x\in\Big(-2 \ ; \ -1\Big]$