Question

solve the following equations (x²-x)²-8(x²+x)+12=0​

Answer 1

Answer is in the above Attachment⬆️

Answer 2

$\huge \fbox \red{Answer}$

The polynomial is

$\rm \pink{(x²−x) 2 −8(x² −x)+12}$

$\rm \pink{y=(x² −x)}$

$\sf \pink{Then \: the \: polynomial \: becomes,}$

$\sf \pink{y ^{2} −8y+12}$

$\sf \pink{=y(y−6)−2(y−6)}$

$\sf \pink{=(y−2)(y−6)}$

$\sf \pink{=(x ^{2} −x−2)(x^{2} −x−6)}$

$\sf \pink{Now \: both \: factors \: can \: be \: further \: factorized,}$

$\sf \pink{(x^{2} −2x+x−2)(x^{2} −3x+2x−6)}$

$\sf \pink{=x(x−2)+1(x−2)} \pink{x(x−3)+2(x−3)}$

$\sf \pink{=(x+1)(x−2)(x+2)(x−3)}$