Răspuns:
Explicație pas cu pas:
E(x) = (x²+2x+3)² - (x²-2x+5)²
folosim formula a²-b² = (a+b)(a-b)
E(x) = (x²+2x+3+x²-2x+5)·(x²+2x+3-x²+2x-5)
E(x) = (2x²+8)(4x-2) = 2·(x²+4)·2(2x-1) = 4·(x²+4)(2x-1) ; (∀)x ∈ R
E(a) = 0 <=> 4·(a²+4)(2a-1) = 0 => 2a - 1 = 0 => a = 1/2
a²+4 > 0 (∀) a ∈ R
