Question

题目最后没拍进去的是数字9

Answer 1

9,最大值是1,再大就是根号下负数了.

10、(1+1/x)(1+1/y)

=(x+1)/x*(y+1)/y

=(xy+x+y+1)/(xy)

=(xy+2)/xy

=1+2/(xy)

=1+2/[x(1-x)]

欲证明(1+1/x)(1+1/y)>=9,

则要证明1+2/[x(1-x)]>=9

即1/[x(1-x)]>=4

因为x>0、y>0且x+y=1,所以0=4x-4x²

4x²-4x+1>=0

(2x-1)²>=0

上式是成立的,所以,(1+1/x)(1+1/y)>=9成立.