Given:

** x>0, y>0, x+y=1 **
Prove that

** (1 + 1/x)(1 + 1/y) ≥ 9. **

(In reply to

Solution by Bractals)

Another way

((x + 1)/x)((y+1)/y) >= 9

xy + x + y + 1 >= 9xy

But x + y = 1,

So we need 2 >= 8xy

or 1/4 >= xy

By symmetry, xy has its maximum when x = y = 1/2,

so the maximum value of xy is 1/4.

q.e.d.