Question

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

If a − b = 4 and a³ − b³ = 124

Answer 1

Here, a − b = 4 and a³ − b³ = 124

Using the identity,

a³ − b³ = (a − b)³ + 3ab(a − b)

124 = (4)³ + 3ab(4)

124 = 64 +12ab

124 − 64 = 12ab

60 = 12ab

`60/12` = ab

∴ ab = 5

Now,

a² + b² = (a − b)² + 2ab

= (4)² + 2(5)

= 16 + 10

∴ a² + b² = 26