Question

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

If a − b = 4, a² + b² = 40

Answer 1

Here, a − b = 4, a² + b² = 40

(a − b)² = a² + b² − 2ab

(4)² = 40 − 2ab

16 = 40 − 2ab

2ab = 40 − 16

2ab = 24

ab = `24/2`

∴ ab = 12

Now,

a³ − b³ = (a − b)³ + 3ab(a − b)

= (4)³ + 3(12)(4)

= 64 + 3(48)

= 64 + 144

∴ a³ − b³ = 208