Question

СРОЧНО ЗНАЙТИ ЗНАЧЕННЯ ВИРАЗУ ДАЮ 20 БАЛЛОВ!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answer 1

$\sqrt{(\frac{1+\sqrt2}{1-\sqrt2})^2+2+(\frac{1-\sqrt2}{1+\sqrt2})^2}=\sqrt{\frac{1+2\sqrt2+2}{1-2\sqrt2+2}+2+\frac{1-2\sqrt2+2}{1+2\sqrt2+2}}=\\\\\sqrt{\frac{3+2\sqrt2}{3-2\sqrt2}+2+\frac{3-2\sqrt2}{3+2\sqrt2}}=\sqrt{\frac{(3+2\sqrt2)^2}{(3-2\sqrt2)(3+2\sqrt2)}+2+\frac{(3-2\sqrt2)^2}{(3-2\sqrt2)(3+2\sqrt2)}}=\\\\\sqrt{\frac{9+12\sqrt2+8}{9-8}+2+\frac{9-12\sqrt2+8}{9-8}}=\sqrt{17+12\sqrt2+2+17-12\sqrt2}=\sqrt{36}=6$