Question

若a+b=2倍的根号下ab,(a>0,b>0),求根号下(3a+5b)分之根号下a+b的值

Answer 1

a+b=2√ab;==>

(√a)^2-2√ab+(√b)^2=0;==>

(√a-√b)^2=0==>a=b;

√(a+b)/√(3a+5b)=√2a/√8a=1/2;

根号下(3a+5b)分之根号下a+b的值为1/2;