\(\left(x^2-4x\right)^2+2\left(x-2\right)^2=43\)
\(\Leftrightarrow\left(x^2-4x\right)^2+2\left(x^2-4x+4\right)=43\)
Đặt \(x^2-4x=t\) ta có:
\(t^2+2\left(t+4\right)=43\)\(\Leftrightarrow t^2+2t-35=0\)
\(\Leftrightarrow\left(t-5\right)\left(t+7\right)=0\)\(\Leftrightarrow\left[{}\begin{matrix}t=5\\t=-7\end{matrix}\right.\)
*)Xét \(t=5\Leftrightarrow x^2-4x=5\)
\(\Leftrightarrow\left(x+1\right)\left(x-5\right)=0\)\(\Leftrightarrow\left[{}\begin{matrix}x=-1\\x=5\end{matrix}\right.\)
*)Xét \(t=-7\Leftrightarrow x^2-4x=-7\)
\(\Leftrightarrow\left(x-2\right)^2+3>0\forall x\) (Loại)
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