Question

[Mãi là Army]

Tìm x biết: (x^2+2x)^2-2x^2-4x=3

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Answer 1

[Lấp La Lấp Lánh]

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

\(\Rightarrow x^4+4x^3+4x^2-2x^2-4x=3\)

\(\Rightarrow x^4+4x^3+2x^2-4x-3=0\)

\(\Rightarrow x^3\left(x-1\right)+5x^2\left(x-1\right)+7x\left(x-1\right)+3\left(x-1\right)=0\)

\(\Rightarrow\left(x-1\right)\left(x^3+5x^2+7x+3\right)=0\)

\(\Rightarrow\left(x-1\right)\left[x^2\left(x+1\right)+4x\left(x+1\right)+3\left(x+1\right)\right]=0\)

\(\Rightarrow\left(x-1\right)\left(x+1\right)\left(x^2+4x+3\right)=0\)

\(\Rightarrow\left(x-1\right)\left(x+1\right)\left[x\left(x+3\right)+\left(x+3\right)\right]=0\)

\(\Rightarrow\left(x-1\right)\left(x+1\right)\left(x+3\right)\left(x+1\right)=0\)

\(\Rightarrow\left[{}\begin{matrix}x=1\\x=-1\\x=-3\end{matrix}\right.\)