The cube of the sum of two given numbers is 1728, while the product of the two given numbers is 32. Find the positive difference between the cubes of the two given numbers.
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 448.
Let two numbers be a and b.
According to the given question,
(a + b)3 = 1728
⇒ (a + b) =12 .......(1)
Also, a × b = 32 ........(2)
Solving equation (1) and (2),
⇒ a = 8 and b = 4
So, a3 - b3 = 83 - 43
⇒ 512 - 64 = 448
Hence, positive difference between the cubes of the two given numbers, a3 - b3 is 448.