If a−b=−7 and a
2
+b
2
=85, then find ab.

We can use the algebraic identity:
(a−b)
2
=a
2
+b
2
−2ab
We are given a−b=−7 and a
2
+b
2
=85. Substitute these values into the identity:

(−7)
2
=85−2ab
49=85−2ab
Rearrange to solve for 2ab:

2ab=85−49
2ab=36
ab=
2
36
​
=18