Question

решить
sqrt{11-4 sqrt{7} } + sqrt{16- 6sqrt{7} }

505f8bf09dc6576abe012cf594b8b23f.doc

Answer 1

$sqrt{11-4 sqrt{7}}+ sqrt{16-6 sqrt{7}}= sqrt{7-2*2 sqrt{7}+4}+sqrt{9-2*3*sqrt{7}+7}= \ =sqrt{(sqrt{7})^2-2*2 sqrt{7}+2^2}+sqrt{3^2-2*3*sqrt{7}+(sqrt{7})^2}= \ =sqrt{(sqrt{7}-2)^2}+sqrt{(3- sqrt{7})^2}=|sqrt{7}-2|+|3- sqrt{7}|= \ =sqrt{7}-2+3- sqrt{7}=1$