ĐK: \(x\ge1\)
\(\sqrt{x^4-2x+1}=x-1\)
\(\Leftrightarrow x^4-2x+1=\left(x-1\right)^2\)
\(\Leftrightarrow x^4-2x+1=x^2-2x+1\)
\(\Leftrightarrow x^4-x^2=0\)
\(\Leftrightarrow x^2\left(x^2-1\right)=0\)
\(\Leftrightarrow x^2\left(x-1\right)\left(x+1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\left(loai\right)\\x=1\left(chon\right)\\x=-1\left(loai\right)\end{matrix}\right.\)
Vậy pt có nghiệm duy nhất \(x=1\)
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