Question

If a -­ b = 6 and ab =16, then a3 -­ b3 is

A) 504 B) 702 C) 728 D) 511

Answer 1

Answer:

Option A : 504

Step-by-step explanation:

a - b = 6

Squaring on both sides,

(a - b)² = 6²

a² + b² - 2ab = 36

a² + b²  = 36 + 2ab

Using ab = 16,

a² + b²  = 36 + 2 * 16

a² + b²  = 36 + 32

a² + b²  = 68  

a³ - b³ = (a – b) (a² + ab + b² )

a³ - b³ = (6) * (a²  + b² + ab )

a³ - b³ = (6) * (68 + 16 )

a³ - b³ = (6) * (84 )

a³ - b³ = 504