\(x^4-4x^3+4x^2+4x^3-16x^2+16x+12x^2-48x+48=0\)
\(\Leftrightarrow x^2\left(x^2-4x+4\right)+4x\left(x^2-4x+4\right)+12\left(x^2-4x+4\right)=0\)
\(\Leftrightarrow\left(x^2+4x+12\right)\left(x-2\right)^2=0\)
\(\Rightarrow x=2\)
b/ ĐKXĐ: ...
\(\Leftrightarrow x^2+\left(\frac{x}{x-1}\right)^2+2x.\frac{x}{x-1}-\frac{2x^2}{x-1}=1\)
\(\Leftrightarrow\left(x+\frac{x}{x-1}\right)^2-\frac{2x^2}{x-1}-1=0\)
\(\Leftrightarrow\left(\frac{x^2}{x-1}\right)^2-\frac{2x^2}{x-1}-1=0\)
Đặt \(\frac{x^2}{x-1}=a\) ta được:
\(a^2-2a-1=0\Rightarrow\left[{}\begin{matrix}a=1+\sqrt{2}\\a=1-\sqrt{2}\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}\frac{x^2}{x-1}=1+\sqrt{2}\\\frac{x^2}{x-1}=1-\sqrt{2}\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x^2-\left(1+\sqrt{2}\right)x+1+\sqrt{2}=0\\x^2+\left(\sqrt{2}-1\right)x-\sqrt{2}+1=0\end{matrix}\right.\)
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