\((5x^2-2x+1)^{2}=(4x-1)^{2}(x^2+1)\)
\(\Leftrightarrow (16x^{2}-8x+1)(x^{2}+1)=25x^{4}+4x^{2}+1-20x^{3}+10x^{2}-4x\)
\(\Leftrightarrow 16x^{4}+16x^{2}-8x^{3}-8x+x^{2}+1=25x^{4}+4x^{2}+1-20x^{3}+10x^{2}-4x\)
\(\Leftrightarrow 16x^{4}+17x^{2}-8x^{3}-8x-25x^{4}-14x^{2}+20x^{3}+4x=0\)
\(\Leftrightarrow -9x^{4}+3x^{2}+12x^{3}-4x=0\)
\(\Leftrightarrow -x(9x^{3}-3x-12x^{2}+4)=0\)
\(\Leftrightarrow -x(3x(3x^{2}-1)-4(3x^{2}-1))=0\)
\(\Leftrightarrow x(3x^{2}-1)(3x-4)=0\)
\(\Rightarrow \left\{\begin{matrix}
x=0\\
x=\pm \frac{\sqrt{3}}{3}\\
x=\frac{4}{3}\\
\end{matrix}\right.\)
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