Question

E(x) = (x² + x +1)² - (x² + x)² - x², unde x ∈ R. Aratati ca E(n) este patrat perfect, pentru orice numar natural n

Answer 1

x^4 + x^3 + x^2 + x^3 + x^2 + x + x^2 + x + 1
= x^4 + 2x^3 + 3x^2 + 2x + 1

x^4 + 2x^3 + x^2

x^4 + 2x^3 + 3x^2 + 2x + 1 - x^4 - 2x^3 - x^2 - x^2 =
x^2 + 2x + 1 =
(x+1)^2 pătrat perfect