If x^2+y^2=36 and (x+y)^2=64 then what is the value of xy?

Question

If x^2+y^2=36 and (x+y)^2=64 then what is the value of xy?

(A) 7

(B) 14

(C) 28

(D) 100

The answer is B, but I still did not find this helpful to work backwards.

Any help?

Answer 1

We're given that:

[a] x² + y² = 36

and

[b] (x + y)² = 64

Let's expand [b]:

(x + y)² = x² + 2xy + y² = 64

Now let's subtract [a] from expanded [b]:

( x² + 2xy + y² ) - ( x² + y² )= 64 - 36

So:

x² + 2xy + y² - x² - y² = 28

Then 2xy = 28, so xy = 28 / 2 = 14.