Question

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

If a + b = 8 and a³ + b³ = 152

Answer 1

Here, a + b = 8, a³ + b³ = 152

Using the identity,

a³ + b³ = (a + b)³ − 3ab(a + b)

152 = (8)³ − 3ab(8)

152 = 512 − 24ab

24ab = 512 − 152

24ab = 360 

∴ ab = `360/24`

∴ ab = 15

Now, 

a² + b² = (a + b)² − 2ab

= (8)2 − 2(15)

= 64 − 30

∴ a² + b² = 34