Question

se considera E(x)=(2x-3)²+2(5-2x)(2x-3)+(5-2x)²,unde x este numar real.
Arătați ca E(x)=4,pentru orice numar real x.

Answer 1

E(x)=(2x-3)²+2(5-2x)(2x-3)+(5-2x)²
Se restrange sub forma de patrat perfect:
E(x)=(2x-3+5-2x)²
E(x)=(5-3)²
E(x)=2²
E(x)=4 ∀ x∈ R