Let x and y be positive real numbers such that . Prove that
(a) ; and
(b) .
a) is positive because y>0, hence
Because LHS is greater than 0 ( x and y are positive real numbers ) hence
x-y > 0 and x>y
b) x,y< 1
Hence (1)and
(2)
Take away (2) from (1) and factorise
Now x > y hence and we can divide both side by and get the desired inequality