Question

tim x:

(5x^2+3x-2)^2=(4x^2-3x-2)^2

Answer 1

\(\left(5x^2+3x-2\right)^2=\left(4x^2-3x-2\right)^2\)

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

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

\(\Leftrightarrow\left(x^2+6x\right)\left(9x^2-4\right)=0\)

\(\Leftrightarrow x\left(x+6\right)\left(3x-2\right)\left(3x+2\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x+6=0\\3x-2=0\\3x+2=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x=-6\\x=\dfrac{2}{3}\\x=-\dfrac{2}{3}\end{matrix}\right.\)