Hi

Bunuel,

Can you please elaborate on how st 2 is not sufficient ?

x - y = 9

( \sqrt{x} + \sqrt{y} ) ( \sqrt{x} - \sqrt{y} ) = 9 = 9 . 1 OR 3. 3

Since it's given the x> y >0, sum of two numbers cannot be equal to difference of the same two numbers. So 3,3 is out. So 9, 1 is still left.

Both numbers positive, one greater than the other,

so

\sqrt{x} + \sqrt{y} = 9

\sqrt{x} - \sqrt{y} = 1

this can be solved and we get the ans which obviously i wrong as per OA.

What's wrong here and why is 2 not sufficient?

Thanks.

You are assuming that \(\sqrt{x} + \sqrt{y}\) and \(\sqrt{x} - \sqrt{y}\) are integers, which is not given. Why cannot \(\sqrt{x} + \sqrt{y}\) be 81 and \(\sqrt{x} - \sqrt{y}\) be 1/9? x - y = 9 has infinitely many solutions, so you cannot get the single numerical value of \(\sqrt{x} - \sqrt{y}\)