已知a>o,b>0a+b=1,求y=(a+1/a)(b+1/b)的最小值证明:(a+1/a)(b+1/b)=ab+a/b+1/ab+b/a =((ab)^2+a^2+1+b^2)/ab =[(ab)^2+(1-2ab)+1]/ab =[(ab-1)^2+1]/ab a+b=1 ab

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已知a>o,b>0a+b=1,求y=(a+1/a)(b+1/b)的最小值证明:(a+1/a)(b+1/b)=ab+a/b+1/ab+b/a=((ab)^2+a^2+1+b^2)/ab=[(ab)^2+

已知a>o,b>0a+b=1,求y=(a+1/a)(b+1/b)的最小值证明:(a+1/a)(b+1/b)=ab+a/b+1/ab+b/a =((ab)^2+a^2+1+b^2)/ab =[(ab)^2+(1-2ab)+1]/ab =[(ab-1)^2+1]/ab a+b=1 ab
已知a>o,b>0a+b=1,求y=(a+1/a)(b+1/b)的最小值
证明:
(a+1/a)(b+1/b)
=ab+a/b+1/ab+b/a
=((ab)^2+a^2+1+b^2)/ab
=[(ab)^2+(1-2ab)+1]/ab
=[(ab-1)^2+1]/ab
a+b=1
ab

已知a>o,b>0a+b=1,求y=(a+1/a)(b+1/b)的最小值证明:(a+1/a)(b+1/b)=ab+a/b+1/ab+b/a =((ab)^2+a^2+1+b^2)/ab =[(ab)^2+(1-2ab)+1]/ab =[(ab-1)^2+1]/ab a+b=1 ab
a*a+b*b>=2ab,a+b=1,a*a+2ab+b*b=1,ab=2*根号下(ab*1/ab)+2ab/ab=2+2=4
y最小值是4