\(4x^4-10x^3+8x^2-5x-1=0\)
\(\left(x^4-x^3+2x^2\right)-\left(4x^3-4x^2+8x\right)+\left(2x^2-2x+4\right)=0\)
\(x^2\left(x^2-x+2\right)-4x\left(x^2-x+2\right)+2\left(x^2-x+2\right)=0\)
\(\left(x^2-x+2\right)\left(x^2-4x+2\right)=0\)
\(\left[\left(x-\frac{1}{2}\right)^2+\frac{7}{4}\right]\left(x^2-4x+2\right)=0\)
Vì \(\left[\left(x-\frac{1}{2}\right)^2+\frac{7}{4}\right]>0\)\(\Rightarrow x^2-4x+2=0\)
\(\Rightarrow\left(x-2\right)^2=2\)\(\Rightarrow x-2=\pm\sqrt{2}\)
\(\Rightarrow\orbr{\begin{cases}x=\sqrt{2}+2\\x=2-\sqrt{2}\end{cases}}\)
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