Question

Tìm x biết:

(x-2)^2-4x^2-4x-1=0

Answer 1

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

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

\(\Leftrightarrow\)\(\left(x-2\right)^2-\left(2x+1\right)^2=0\)

\(\Leftrightarrow\)\(\left(x-2-2x-1\right)\left(x-2+2x+1\right)=0\)

\(\Leftrightarrow\)\(\left(-x-3\right)\left(3x-1\right)=0\)

\(\Leftrightarrow\)\(\orbr{\begin{cases}-x-3=0\\3x-1=0\end{cases}\Leftrightarrow\orbr{\begin{cases}x=-3\\x=\frac{1}{3}\end{cases}}}\)

Vậy \(x=-3\) hoặc \(x=\frac{1}{3}\)

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