Question

упростить выражение

$frac{1- sqrt{10} }{ sqrt{2} + sqrt{5} } + frac{7}{2 sqrt{2}+1 }-(11- 5sqrt{5})(2+ sqrt{5})$

Answer 1

$frac{1-sqrt{10}}{sqrt{2}+sqrt{5}}+frac{7}{2sqrt{2}+1}-(11-5sqrt{5})(2+sqrt{5})=\\ frac{(sqrt{5}-sqrt{2})(1-sqrt{10})}{3}+frac{7(2sqrt{2}-1)}{7}-(sqrt{5}-3)=\\ frac{21sqrt{5}-42sqrt{2}}{21}+frac{42sqrt{2}-21}{21}-frac{21(sqrt{5}-3)}{21}=\\ frac{42}{21}=2$