The sum of the cubes of two given natural numbers is 9728, while the sum of…
2023
The sum of the cubes of two given natural numbers is 9728, while the sum of the twogiven numbers is 32. What is the product of the two given numbers?
Answer: C. 240 — Let the numbers be a and b. Given a + b = 32 and a^3 + b^3 = 9728. Since a^3 + b^3 = (a + b)^3 - 3ab(a + b), we get 9728 = 32768 - 96ab, so ab = 240.
- A.
160
- B.
320
- C.
240
- D.
200
Attempted by 10 students.
Show answer & explanation
Correct answer: C
Let the numbers be a and b. Given a + b = 32 and a^3 + b^3 = 9728. Since a^3 + b^3 = (a + b)^3 - 3ab(a + b), we get 9728 = 32768 - 96ab, so ab = 240.
Loading lesson…