Question
Download Solution PDFThe cube of the difference between two given natural numbers is 1728, while the product of these two given numbers is 108. Find the positive difference between the cubes of these two given numbers.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
(1st natural number - 2nd natural number)3 = 1728
1st natural number × 2nd natural number = 108
Formula used:
(A - B)3 = A3 - B3 - 3AB × (A - B)
Calculation:
Let 1st natural number = A
2nd natural number = B
(A - B)3 = 1728
⇒ (A - B) = 3√1728 = 12
A3 - B3 = (A - B)3 + 3AB × (A - B)
⇒ 1728 + 3 × 108 × 12
⇒ 1728 + 3 × 108 × 12
⇒ 1728 + 3888 = 5616
∴ The correct answer is 5616.
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