Question

Найдите значение выражения $sqrt{21+4 sqrt{17} }+ sqrt{21-4 sqrt{17} }$

Answer 1

$sqrt{21+4sqrt{17}}+ sqrt{21-4sqrt{17}}=sqrt{4+4sqrt{17}+17}+sqrt{4-4sqrt{17}+17}= \ =sqrt{2^2+2cdot2sqrt{17}+(sqrt{17})^2}+sqrt{2^2-2cdot2sqrt{17}+(sqrt{17})^2}= \ =sqrt{(2+sqrt{17})^2}+sqrt{(2-sqrt{17})^2}=(2+sqrt{17})+|2-sqrt{17}|= \ =2+sqrt{17}+sqrt{17}-2=2sqrt{17}.$