Question

(x+1)² = 4(x²-2x+1)²

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^{bơi vô làm hộ vs}

Answer 1

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

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

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

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

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

\(\Leftrightarrow\left[{}\begin{matrix}-2x^2+5x-1=0\\2x^2-3x+3=0\left(loai\right)\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{5+\sqrt{17}}{4}\\x=\dfrac{5-\sqrt{17}}{4}\end{matrix}\right.\)