If x + y = 7 and x2 + y2 = 25, then which one of the following equals the value of x3 + y3 ?

If x + y = 7 and x² + y² = 25, then which one of the following equals the value of x³ + y³ ?

A 25

B 35

C 65

D 91

Correct Answer: Option D

Solution:

দেয়া আছে, x² + y² = 25

=> x² + y² = 25

=> (x + y)² - 2xy = 25

=> 7² - 2xy = 25

=> 2xy = 24

xy = 12

x³ + y³ = (x + y)³ - 3xy (x + y)

= 7 - 3 \( \times \) 12 \( \times \) 7 = 343 - 252 = 91