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Aratati ca numarul a ∈ N, daca a = (√3-1)² + (√3-1)(√3+1)+(√3+1)²

Răspuns :

a = (√3-1)² + (√3-1)(√3+1)+(√3+1)²=
=3-2√3+1+3-1+3+2√3+1=
=3+3+3+1=10

(a-b)²=a²+b²-2ab
(a+b)²=a²+b²+2ab