Question

$frac{1}{5+2 sqrt{6} } + frac{1}{5-2 sqrt{6} }$
$frac{ sqrt{5- sqrt{3} } }{ sqrt{5+ sqrt{3} } } + frac{ sqrt{5+ sqrt{3} } }{ sqrt{5- sqrt{3} } }$
$frac{9+3 sqrt{a}+a}{3+ sqrt{a} }$
Решите подробнее пожалуйста

Answer 1

$frac{1}{5+2sqrt6}+frac{1}{5-2sqrt6}=frac{5-2sqrt6+5+2sqrt6}{(5+2sqrt6)(5-2sqrt6)}=frac{10}{25-4cdot 6}=10\\\frac{sqrt{5-sqrt3}}{sqrt{5+sqrt3}}+frac{sqrt{5+sqrt3}}{sqrt{5-sqrt3}}=frac{5-sqrt3+5+sqrt3}{sqrt{(5-sqrt3)(5+sqrt3)}}=frac{10}{sqrt{25-3}}=frac{10}{sqrt{22}}=frac{10sqrt{22}}{22}=frac{5sqrt{22}}{11}\\\frac{9+3sqrt{a}+a}{3+sqrt{a}}=frac{(3-sqrt{a})(9+3sqrt{a}+a)}{(3+sqrt{a})(3-sqrt{a})}=frac{3^3-(sqrt{a})^3}{9-a}=frac{27-sqrt{a^3}}{9-a}$