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Question : The 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.

Option 1: 4104

Option 2: 5616

Option 3: 2160

Option 4: 5626


Team Careers360 1st Jan, 2024
Answer (1)
Team Careers360 5th Jan, 2024

Correct Answer: 5616


Solution : Given: The cube of the difference between two given natural numbers is 1728, while the product of these two given numbers is 108.
Let the two numbers be $a$ and $b$.
So, $(a–b)^3=1728$ and $ab=108$.
Now, $a^3–b^3=(a–b)^3+3ab(a–b)$
⇒ $a^3–b^3=1728+3×108(12)$
⇒ $a^3–b^3=1728+3888$
⇒ $a^3–b^3=5616$
Hence, the correct answer is 5616.

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