Question

Найдите целое число равное разности

Answer 1

$\sqrt{|40\sqrt2-57|} -\sqrt{40\sqrt2+57}= \sqrt{|-(57-40\sqrt2)|} -\sqrt{57+40\sqrt2}=$$=\sqrt{|-(5^2-2\cdot5\cdot4\sqrt2+(4\sqrt2)^2)|}-\sqrt{5^2+2\cdot5\cdot4\sqrt2+(4\sqrt2)^2}=$$=\sqrt{|-(5-4\sqrt2)^2|}-\sqrt{(5+4\sqrt2)^2}=\sqrt{(5-4\sqrt2)^2}-\sqrt{(5+4\sqrt2)^2}=$$=|5-4\sqrt2|-|5+4\sqrt2|=4\sqrt2-5-5-4\sqrt2=-10$.