x+y=4,求(x+1/x)(y+1/y)的minx,y属于正数
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x+y=4,求(x+1/x)(y+1/y)的minx,y属于正数
x+y=4,求(x+1/x)(y+1/y)的min
x,y属于正数
x+y=4,求(x+1/x)(y+1/y)的minx,y属于正数
(x+1/x)(y+1/y)
=(x^2+1)(y^2+1)/xy
=[(xy)^2+(x^2+y^2)+1]/xy
=[(xy)^2+(x+y)^2-2xy+1]/xy
=[(xy)^2+17-2xy]/xy
=xy+17/xy -2
≥2√17-2
当且仅当xy=17/xy,xy=√17时取等号
故最小值是2√17-2
f(x,y)=xy+1/(xy)+x/y+y/x,
用这个公式a+b大于或等于2*根号(ab)
等号当a=b时候成立
xy+1/(xy),x/y+y/x都可以用
是求(x+1/x)(y+1/y)两个式子中比较小的一个?
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