Let x and y be positive real numbers such that . Prove that

(a) ; and

(b) .

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- October 24th 2008, 01:40 AMalexmahoneLet x and y be positive real numbers...
Let x and y be positive real numbers such that . Prove that

(a) ; and

(b) . - October 24th 2008, 08:07 AMPlato
From the given, , we get

.

From the above we get

.

Do you see ho to finish? - October 26th 2008, 06:09 AMsimple_life_vu
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