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2022-05-31 13:51:56
\(\sqrt{1-\sqrt{x^4-x^2}}=x-1\)
\(\Leftrightarrow1-\sqrt{x^4-x^2}=\left(x-1\right)^2\)
\(\Leftrightarrow-\sqrt{x^4-x^2}=x^2-2x+1-1\)
\(\Leftrightarrow x^4-x^2=\left(x^2-2x\right)^2\)
\(\Leftrightarrow x^4-x^2=x^4-4x^3+4x^2\)
\(\Leftrightarrow4x^3-5x^2=0\)
\(\Leftrightarrow x^2\left(4x-5\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x^2=0\\4x-5=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x=\dfrac{5}{4}\end{matrix}\right.\)
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