Корень из(х-4)^2+корень из(х+4)^2=2х

[latex] \sqrt{(x-4)^2 } +\sqrt{(x+4)^2} =2x \\ |x-4|+|x+4|=2x \\ 1)x \geq 4 \\ x-4+x+4=2x\iff 2x=2x\iff 0=0 \\ x\in[4;+\infty) \\ \\ 2)-4 \leq x \ \textless \ 4 \\ \\ -x+4+x+4=2x\iff 2x=8 \iff x=4 \notin[-4;4) \\ \\ 3)x\ \textless \ -4 \\ \\ -x+4-x-4=2x\iff -2x+8=2x\iff 4x=8 \\ x=2\notin (-\infty;-4)[/latex]