Question

Urgent!! Va roog!!
Aratati ca numarul a = √(2√3 - 3)2 + 2√(√3-2)2 este natural.

PS: Doiul acela dupa paranteza "√(2√3 - 3)" si cel dupa paranteza "2√(√3-2)" este puterea a doua :) .

Answer 1

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Answer 2

 [tex]a=\underbrace{\sqrt{(2\sqrt3-3)^2}}_{|2\sqrt3-3|} \,+\,\underbrace{2\sqrt{\sqrt3-2)^2}}_{2|\sqrt3-2|} =2\sqrt3-3+2(2-\sqrt3)=\\ =\not2\sqrt3-3+4-\not2\sqrt3=1\,\in\,\mathbb{N}[/tex]