Question

$sqrt{|40 sqrt{2}-57 |} - sqrt{40 sqrt{2}+57 }$
Найдите целое число равное разности

Answer 1

$sqrt{|40sqrt2-57|} -sqrt{40sqrt2+57}= sqrt{|-(57-40sqrt2)|} -sqrt{57+40sqrt2}=$$=sqrt{|-(5^2-2cdot5cdot4sqrt2+(4sqrt2)^2)|}-sqrt{5^2+2cdot5cdot4sqrt2+(4sqrt2)^2}=$$=sqrt{|-(5-4sqrt2)^2|}-sqrt{(5+4sqrt2)^2}=sqrt{(5-4sqrt2)^2}-sqrt{(5+4sqrt2)^2}=$$=|5-4sqrt2|-|5+4sqrt2|=4sqrt2-5-5-4sqrt2=-10$.