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 \(\sqrt{x} - \sqrt{y}\)