1.已知x,y∈R+,且1/x+1/y=1,求2x+y的最小值2.已知:a,b∈R+,求证b/√a+a/√b≥√a+√b.

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1.已知x,y∈R+,且1/x+1/y=1,求2x+y的最小值2.已知:a,b∈R+,求证b/√a+a/√b≥√a+√b.
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1.已知x,y∈R+,且1/x+1/y=1,求2x+y的最小值2.已知:a,b∈R+,求证b/√a+a/√b≥√a+√b.
1.已知x,y∈R+,且1/x+1/y=1,求2x+y的最小值
2.已知:a,b∈R+,求证b/√a+a/√b≥√a+√b.

1.已知x,y∈R+,且1/x+1/y=1,求2x+y的最小值2.已知:a,b∈R+,求证b/√a+a/√b≥√a+√b.
1.2x+y=(2x+y)(1/x+1/y)=3+2x/y+y/x>=3+2根号2(2x/y=y/x时即x=1+0.5*根号2,y=1+根号2时等号成立)
2.由(根号a-根号b)^2>=0知a+b-2*根号ab>=0
除以根号a知:根号a+b/根号a>=2*根号b
即b/根号a>=2*根号b-根号a
同理a/根号b>=2*根号a-根号b
相加得原不等式成立

1.2x+y=(2x+y)(1/x+1/y)=3+2x/y+y/x>=3+2根号2(2x/y=y/x时即x=1+0.5*根号2,y=1+根号2时等号成立)
2.由(根号a-根号b)^2>=0知a+b-2*根号ab>=0
除以根号a知:根号a+b/根号a>=2*根号b
即b/根号a>=2*根号b-根号a
同理a/根号b>=2*根号a-根号b
相加得原不等式成立