51 Views

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.

SSC CGL Complete Guide

Candidates can download this ebook to know all about SSC CGL.

Download EBook

Know More About

Related Questions

TOEFL ® Registrations 2024
Apply
Accepted by more than 11,000 universities in over 150 countries worldwide
Manipal Online M.Com Admissions
Apply
Apply for Online M.Com from Manipal University
View All Application Forms

Download the Careers360 App on your Android phone

Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile

150M+ Students
30,000+ Colleges
500+ Exams
1500+ E-books