0<x<1,a,b为正常数，a2/x+b2/(1-x)的最小值为
热心网友
a2/x+b2/(1-x)=a2(x+1-x)/x+b2(x+1-x)/(1-x)=a2+a2(1-x)/x++b2+b2x/(1-x)=a2+b2+a2(1-x)/x+b2x/(1-x),而a2(1-x)/x+b2x/(1-x)≥2√[a2(1-x)/x]×[b2x/(1-x)]=2ab,所以a2/x+b2/(1-x)最小值为a2+b2+2ab=(a+b)2
热心网友
2（a+b)
0<x<1,a,b为正常数，a2/x+b2/(1-x)的最小值为
a2/x+b2/(1-x)=a2(x+1-x)/x+b2(x+1-x)/(1-x)=a2+a2(1-x)/x++b2+b2x/(1-x)=a2+b2+a2(1-x)/x+b2x/(1-x),而a2(1-x)/x+b2x/(1-x)≥2√[a2(1-x)/x]×[b2x/(1-x)]=2ab,所以a2/x+b2/(1-x)最小值为a2+b2+2ab=(a+b)2
2（a+b)