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
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.
Related Questions
Know More about
Staff Selection Commission Combined Grad ...
Result | Eligibility | Application | Selection Process | Preparation Tips | Admit Card | Answer Key
Get Updates Brochure
Your Staff Selection Commission Combined Graduate Level Exam brochure has been successfully mailed to your registered email id “”.
