Question : The difference between the cubes of two given natural numbers is 6272, while the positive difference between the two given numbers is 8. What is the product of the two given numbers?
Option 1: 160
Option 2: 240
Option 3: 200
Option 4: 320
Correct Answer: 240
Solution :
Let the numbers be x and y.
So, x
3
– y
3
= 6272 and (x – y) = 8
Cubing both sides of the given expression, (x – y) = 8,
⇒ (x – y)
3
= 8
3
⇒ x
3
– y
3
– 3xy(x – y) = 512
⇒ 6272 – 3xy × 8 = 512
⇒ 24xy = 5760
⇒ xy = 240
Hence, the correct answer is 240.
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