Question

Aratati ca: x^4+x^2+1=(x^2-x+1)*(x^2+x+1) pentru orice nr real x

Answer 1

$x^4+x^2+1 =$

$= x^2(x^2+1)+x^2+1-x^2$

$= (x^2+1)(x^2+1)-x^2$

$= (x^2+1)^2-x^2$

$=\big[(x^2+1)-x\big]\big[(x^2+1)+x\big]$

$= (x^2-x+1)(x^2+x+1)$