a,b均为正实数,求证:根号(a/(a+3b))+根号(b/(b+3a))≥1
问题描述：
a,b均为正实数,求证:根号(a/(a+3b))+根号(b/(b+3a))≥1
答
设x=根号(a/(a+3b))+根号(b/(b+3a)),则x^2=(3a^2+3b^2+2ab)/(3a^2+10ab+3b^2)+2根号(ab/(3a^2+10ab+3b^2)),设y=根号(ab/(3a^2+10ab+3b^2)=根号(ab/(3a^2+3b^2+10ab）,其中3a^2+3b^2+10ab=3(a^2+b^2)>=6ab+10ab=16ab,...