X和Y是正数,且2X+Y-2等于0,求U等于XY分X+Y的最小值是多少?
人气：301 ℃ 时间：2019-12-13 17:44:07
解答
2x+y=2
x+y/2=1
u=u*1=(x+y)/xy*1
=(1/y+1/x)(x+y/2)
=x/y+1/2+1+y/(2x)
=3/2+x/y+y/(2x)
x>0,y>0
x/y+y/(2x)>=2√[x/y*y/(2x)]=√2
所以最小值=3/2+√2
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