Răspuns:
Explicație pas cu pas:
a) E(x) = (x+1)² - (-x-1)² + x²+2x+1
E(x) = (x+1)²-[(-1)(x+1)]² + (x+1)²
E(x) = (x+1)²- (x+1)²+ (x+1)²
E(x) = (x+1)² ; (∀) x ∈ R
b) E(x) > x <=> (x+1)² > x =>
x²+2x+1 > x=>
x²+x+1 > 0 ; Δ < 0 =>
x²+x+1 > 0 , (∀) x ∈ R =>
E(x) > x , (∀) x ∈ R
(∀) x = oricare x
