Ian Stewart wrote:

Thonk02 wrote:Whatt is value of: (X+Y) ^2
_________
(X-Y)^2

1. X^2 + Y^2 = 3XY
2. XY = 3


Any ideas?

answer is D.

I expect the question means to ask for the value of:

(x+y)^2
(x-y)^2

and if so, the answer certainly is not D.

If you expand the top and bottom, the expression is equal to:

x^2 + 2xy + y^2
x^2 - 2xy + y^2

And using Statement 1, we can replace x^2 + y^2 on the top and bottom to get:

3xy + 2xy
3xy - 2xy

= 5/1 = 5

Using Statement 2, we won't get the necessary cancellation, so the Statement is insufficient. To be sure, you can plug in any pair of values which satisfy xy = 3; if x = 3 and y = 1, the expression is equal to 4, whereas if x = 2 and y = 3/2, the expression is equal to 49.

So unless I've misunderstood the typography in the question, the answer should be A.