Problem 5 Let x,yx,yx,y be positive real numbers such that x+y=1x+y=1x+y=1 . Prove that (1+1x)(1+1y)≥9\left(1+\frac {1}{x}\right)\left(1+\frac {1}{y}\right)\geq 9(1+x1)(1+y1)≥9 .