SSC CPO 2024 PYQ — Question 120

The correct answer is Option 3 i.e. 756.

Let the two numbers be x and y

Given, x + y = 12 and xy = 27

We know that,

x³ + y³ = (x + y)(x² + y² - xy).....(1)

Also,

⇒ x² + y² = (x + y)² - 2xy

⇒ x² + y² = 12² - 54

⇒ x² + y² = 144 - 54

⇒ x² + y² = 90

Now, put the value in eq 1

⇒ x³ + y³ = (12)(90 - 27)

⇒ x³ + y³ = 12 × 63

⇒ x³ + y³ = 756

Thus, the sum of the cubes is 756