Question

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

If a − b = 7, a² + b² = 65

Answer 1

Here, a − b = 7, a² + b² = 65

(a − b)² = a² + b² − 2ab

(7)² = 65 − 2ab

49 = 65 − 2ab

2ab = 65 − 49

2ab = 16

ab = `16/2`

∴ ab = 8

Now,

a³ − b³ = (a − b)³ + 3ab(a − b)

= (7)³ + 3(8)(7)

= 343 + 3(56)

= 343 + 168

∴ a³ − b³ = 511