If x+y=10 and x
2
+y
2
=68, then find xy.

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

(10)
2
=68+2xy
100=68+2xy
2xy=100−68
2xy=32
xy=
2
32
​
=16