Question

 (x² - x + 2)² - 3(x + 2)² = (x² - x)² - 5x² - 21x

Answer 1

\(\left(x^2-x+2\right)^2-3\left(x+2\right)^2=\left(x^2-x\right)^2-5x^2-21x\)

\(\Leftrightarrow\left(x^2-x+2\right)^2-\left(x^2-x\right)^2-3x^2-12x-4+5x^2+21x=0\)

\(\Leftrightarrow\left(x^2-x+2-x^2+x\right)\left(x^2-x+2+x^2-x\right)+2x^2+9x-4=0\)

\(\Leftrightarrow2\left(2x^2-2x+2\right)+2x^2+9x-4=0\)

\(\Leftrightarrow6x^2+5x=0\)

\(\Leftrightarrow x\left(6x+5\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x=-\dfrac{5}{6}\end{matrix}\right.\)