SSC CGL 2023 PYQ — Question 55

The correct answer is option 3 i.e. 14125.

Given that, x + y = 25

And xy = 20

Also, a³ + b³ = (a + b)(a² - ab + b²)

(a + b)² = a² + 2ab + b²

According to the given question,

(x + y)² = 25²

⇒ x² + 2xy + y² = 625

⇒ x² + 2(20) + y² = 625

⇒ x² +  y² = 625 - 40

⇒ x² + y² = 585

Now, x³ + y³ = (x + y)(x² - xy + y²)

⇒ x³ + y³ = (25)(585 - 20)

⇒ x³ + y³ = 25 × 565

⇒ x³ + y³ = 14125

Hence the required answer is 14125.