Question

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

Answer 1

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