Question

√|-18-8√2|-√|8√2-18|-1/2√32 весь модуль под корнем

Answer 1

$sqrt{|-18-8sqrt{2}|}-sqrt{|8sqrt{2}-18|}-frac{1}{2}sqrt{32}=\ sqrt{|18+8sqrt{2}|}-sqrt{|18-8sqrt{2}|}-frac{1}{2}sqrt{16*2}=\ sqrt{|16+8sqrt{2}+2|}-sqrt{|16-8sqrt{2}+2|}-frac{1}{2}sqrt{16}*sqrt{2}=\ sqrt{|4^2+2*4*sqrt{2}+(sqrt{2})^2|}-sqrt{|4^2-2*4*sqrt{2}+(sqrt{2})^2|}-frac{1}{2}*4*sqrt{2}=\ sqrt{|(4+sqrt{2})^2|}-sqrt{|(4-(sqrt{2}))^2|}-2sqrt{2}=\ |4+sqrt{2}|-|4-sqrt{2}|-2sqrt{2}=\ 4+sqrt{2}-(4-sqrt{2})-2sqrt{2}=\ 4+sqrt{2}-4+sqrt{2}-2sqrt{2}=0$

 

ответ: 0