What is the value of xy if x−y=3 and x
2
+y
2
=15?

We know the algebraic identity:
(x−y)
2
=x
2
+y
2
−2xy
Substitute the given values into the identity:

(3)
2
=15−2xy
9=15−2xy
2xy=15−9
2xy=6
xy=
2
6
​
=3
Hence, the value of xy is 3.