设A>B>0,则A方+1/AB+1/A(A-B)的最小值是?

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设A>B>0,则A方+1/AB+1/A(A-B)的最小值是?

设A>B>0,则A方+1/AB+1/A(A-B)的最小值是?
设A>B>0,则A方+1/AB+1/A(A-B)的最小值是?

设A>B>0,则A方+1/AB+1/A(A-B)的最小值是?
a²+1/ab+1/a(a-b)
=a²-ab+ab+1/ab+1/(a²-ab)
=(a²-ab)+1/(a²-ab)+ab+1/ab
≥2+2=4
当且仅当((a²-ab)²)²=1且(ab)²=1时取等号
解得a=√2,b=1/√2=√2/2