SSC CGL 2022 PYQ — Question 55

The correct answer is Option 1 i.e. 12.

Given:

a – b = 2 and

a³ – b³ = 80

Concept Used:

a³ – b³ = (a - b)(a² + ab + b²)     ..(i)

(a - b)² = a² - 2ab + b²    ....(ii)

Explanation:

From the given question and using equation (i), we get

80 =  2((a² + ab + b²) 

⇒ (a² + ab + b²)  = 40 ....(iii)

Also using equation (ii), we get

a² - 2ab + b² = (2)²

⇒ a² - 2ab + b² = 4  

⇒ a² + b² = 4 + 2ab ....(iv)

Using the values from equation (iv) in equation (iii), we get

(4 + 2ab + ab)  = 40

⇒ 4 + 3ab = 40

⇒ 3ab = 36

⇒ ab = 36/3 = 12

Hence the value of ab is 12.