\(\left(\left|x_1\right|+\left|x_2\right|\right)^2=16\)
\(\Leftrightarrow x_1^2+x_2^2+2\left|x_1x_2\right|=16\)
\(\Leftrightarrow\left(x_1+x_2\right)^2-2x_1x_2+2\left|x_1x_2\right|=16\)
\(\Leftrightarrow m^2-2\left(m-1\right)+2\left|m-1\right|=16\)
TH1: \(m\ge1\) ta được:
\(m^2-2\left(m-1\right)+2\left(m-1\right)=16\Rightarrow\left[{}\begin{matrix}m=4\\m=-4< 1\left(loại\right)\end{matrix}\right.\)
TH2: \(m\le1\) ta được:
\(m^2-2\left(m-1\right)-2\left(m-1\right)=16\)
\(\Leftrightarrow m^2-4m-12=0\Rightarrow\left[{}\begin{matrix}m=6>1\left(loại\right)\\m=-2\end{matrix}\right.\)
Vậy \(\left[{}\begin{matrix}m=4\\m=-2\end{matrix}\right.\)
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