Question

Find the value of ab and a² + b² in the following:

If a − b = 3 and a³ − b³ = 63

Answer 1

Here, a − b = 3, a³ − b³ = 63

Using the identity,

a³ − b³ = (a − b)³ + 3ab(a − b)

63 = (3)³ + 3ab(3)

63 = 27 + 9ab

63 − 27 = 9ab

36 = 9ab

ab = `36/9`

∴ ab = 4

Now,

a² + b² = (a − b)² + 2ab

= (3)² + 2(4)

= 9 + 8

∴ a² + b² = 17