Question

найти корень уравнения | |х|+2 |=7
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Answer 1

$\Big|\, |x|+2\, \Big|=7\ \ \Rightarrow \ \ \ |x|+2=\pm 7\\\\a)\ \ |x|+2=7\ \ \to \ \ |x|=5\ \ ,\ \ x\pm 5\\\\b)\ \ |x|+2=-7\ \ \to \ \ \ |x|=-9<0\ (!!!)\ \ \to \ \ x\in \varnothing \ ,\ \ tak\ kak\ |x|\geq 0\ (!!!)\\\\Otvet:\ \ x_1=-5\ ,\ x_2=5\ .$