Question

aratati ca numarul a=sqrt(3 - 2sqrt(2)) - sqrt(2) este intreg

Answer 1

Salut,

$a=\sqrt{3-2\sqrt2}-\sqrt2=\sqrt{2-2\sqrt2\cdot 1+1}-\sqrt2=\sqrt{(\sqrt2)^2-2\sqrt2\cdot 1+1^2}-\sqrt2=\\=\sqrt{(\sqrt2-1)^2}-\sqrt2=|\sqrt2-1|-\sqrt2=\sqrt2-1-\sqrt2=-1\in\mathbb{Z}.$

Simplu, nu ?
Green eyes.