Question

2. Tìm x biết : \(\left(x^2-1\right)^2=4x+1\)

Answer 1

\(\left(x^2-1\right)^2=4x+1\)

\(\Leftrightarrow x^4-2x^2+1=4x+1\)

\(\Leftrightarrow x^4-2x^2-4x=0\)

\(\Leftrightarrow x\left(x^3-2x-4\right)=0\)

\(\Leftrightarrow x\left[x^2\left(x-2\right)+2x\left(x-2\right)+2\left(x-2\right)\right]=0\)

\(\Leftrightarrow x\left(x-2\right)\left(x^2+2x+2\right)=0\)

Vì \(x^2+2x+2=\left(x+1\right)^2+1\ge1>0\forall x\)

\(\Rightarrow\left[{}\begin{matrix}x=0\\x-2=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x=2\end{matrix}\right.\)

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