Question

E(x) =(x^2 -x+2)^2- (x^2-x)^2-(2x-1)^2
Determination CA E(x)=3 oricare AR fi x in multimea R

Answer 1

E(x) = (x^2 - x + 2)^2 - (x^2-x)^2 - (2x-1)^2 = 
       = (x^2 - x + 2)(x^2 - x + 2) - (x^4-2x^3+x^2) - (4x^2-4x+1) =
       = x^4 - x^3 + 2x^2 - x^3 +x^2 - 2x + 2x^2 - 2x + 4 - x^4 + 2x^3 - x^2 - 4x^2 + 4x - 1 = 
       = (x^4 - x^4) + (-x^3 -x^3 + 2x^3) + (2x^2 + x^2 + 2x^2 - x^2 - 4x^2) + (-2x -2x + 4x) + (4-1) = 
       = 3