The sum of the cubes of two natural numbers is 9728, while the sum of these two numbers is 32. What is the product of these two numbers?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is Option 3 i.e. 240.
a3 + b3 = 9728
a + b = 32
(a + b)3 = a3 + b3 + 3ab(a + b)
⇒ 323 = 9728 + 3ab(32)
⇒ 32768 = 9728 + 3ab(32)
⇒ 3ab(32) = 23040
⇒ 3ab = 720
⇒ ab = 240