If a−b=−5 and a
2
+b
2
=73, then find ab.

We use the algebraic identity:
(a−b)
2
=a
2
+b
2
−2ab
Given:

a−b=−5

a
2
+b
2
=73

Substitute these values into the identity:

(−5)
2
=73−2ab
25=73−2ab
Rearranging the terms to find 2ab:

2ab=73−25
2ab=48
ab=
2
48
​
=24