(х^2-х+1)(х^2-х-7)=65

Question

(х^2-х+1)(х^2-х-7)=65

Answer 1

X²-x=t ⇒ (t+1)(t-7)=65
t²-7t+t-7-65=0
t²-6t-72=0

Answer 2

(x^2-x+1)(x^2-x-7)=65 x^4-x^3-7x^2-x^3+x^2+7x+x^2-x-7=65 x^4-2x^3-5x^2-6x=72 x^4-2x^3+x^2-6x^2-6x=72 (x^2-x)^2-6(x^2-x)=72 (x^2-x)(x^2-x-6)=72 x(x-1)(x^2-x-6)=72