If a – b = 2 and a³ – b³ = 80, then what will be the value of ab?

Correct option is A

Given:

a - b = 2

a³ - b³ = 80

Formula Used:

We use the identity for the difference of cubes:

a³ - b³ = (a - b)(a² + ab + b²)

Solution:

Using the identity:

a³ - b³ = (a - b)(a² + ab + b²)

Substituting a - b = 2 into the equation:

80 = 2(a² + ab + b²)

a² + ab + b² = 40 ………… equation (1)

From this a² + b² = (a - b)² + 2ab……….

a² + b² = 4 + 2ab

Put the value of  a² + b²   in equation (1)

4 + 2ab + ab = 40

4 + 3ab = 40

3ab = 40 - 4 = 36

ab = 36 / 3 = 12

Thus, the value of ab is 12.