If x - y = 11 and 1/x - 1/y = 11/24 , then what is the value of x³ - y³+ x²y²?

If x - y = 11 and 1/x - 1/y = 11/24 , then what is the…

If x - y = 11 and $\frac{1}{x}$ - $\frac{1}{y}$ = $\frac{11}{24}$ , then what is the value of x³ - y³+ x²y²?

Show answer & explanation

Correct answer: D

Explanation

The correct answer is option 4 i.e. 1115.

1/x - 1/y = 11/24

⇒ (y - x)/xy = 11/24

⇒ -(x - y)/xy = 11/24

⇒ -11/xy = 11/24

⇒ xy = -24

⇒ x³ - y³ + x²y² = (x - y)³ + 3xy (x - y) + (xy)²

⇒ (11)³ + 3(-24) × 11 + 576

⇒ 1331 - 792 + 576

⇒ 539 + 576 = 1115