Question

Aratati ca numarul a=\sqrt{9-4\sqrt{2}} - 2\sqrt{2} este intreg.

Answer 1

[tex]a=\sqrt{9-4\sqrt2}-2\sqrt 2\\ a=\sqrt{8-4\sqrt2+1}-2\sqrt 2\\ a=\sqrt{(2\sqrt2-1)^2}-2\sqrt 2\\ a=|2\sqrt2-1|-2\sqrt2\\ a=2\sqrt2-1-2\sqrt2= -1\in \mathbb{Z}[/tex]