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已知x>y>0,求x2+64/y(x-y)的最小值
人气:486 ℃ 时间:2020-09-22 15:05:17
解答
x2+64/y(x-y)
=(x-y+y)^2+64/y(x-y)
=(x-y)^2+y^2+2y(x-y)+64/y(x-y)
因为(x-y)^2+y^2>=2y(x-y)
所以原式>=4y(x-y)+64/y(x-y)>=2根号(4*64)=2*2*8=32
当且仅当:x-y=y,4y(x-y)=64/y(x-y)时取等号,此时y=2,x=4
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