Question

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

Answer 1

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

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

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

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

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

\(\Leftrightarrow\left(x^2+2x-2\right)\left[\left(x-\dfrac{1}{2}\right)^2+\dfrac{3}{4}\right]=0\)

\(\Leftrightarrow x^2+2x-2=0\) (bấm máy)