Question

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

If a + b = 8, a² + b² = 34

Answer 1

Here, a + b = 8, a² + b² = 34

Using the identity,

(a + b)² = a² + b² + 2ab

(8)² = 34 + 2ab

64 = 34 + 2ab

64 − 34​ = 2ab

30 = 2ab

`30/2` = ab

∴ ab = 15

Now,

a³ + b³ = (a + b)³ − 3ab(a + b)

= (8)³ − 3(15)(8)

= 512 − 3(120)

= 512 − 360

∴ a³ + b³ = 152