已知正实数ab和正实数xy满足a+b=13,a/x+b/y=1,x+y的最小值是25,求a,b的值
人气：416 ℃ 时间：2020-01-09 06:13:14
解答
解(x+y)(a/x+b/y)=a+b+ay/x+bx/yay/x+bx/y>=2√(ay/x*bx/y)=2√(ab)所以(x+y)(a/x+b/y)>=a+b+2√(ab)=13+2√(ab)因为a/x+b/y=1所以x+y最小值=13+2√(ab)=25ab=36a+b=13a>0,b>0所以a=4,b=9或a=9,b=4...
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