Question

Find the value of ab and a³ + b³ in the following:

If a + b = 9, a² + b² = 53

Answer 1

Here, a + b = 9, a² + b² = 53

Using the identity,

(a + b)² = a² + b² + 2ab

(9)² = 53 + 2ab

81 − 53 = 2ab

28 = 2ab

`28/2` = ab

∴ ab = 14

Now,

a³ + b³ = (a + b)³ − 3ab(a + b)

= (9)³ − 3(14)(9)

= 729 − 3(126)

= 729 − 378

∴ a³ + b³ = 351