25 Views

Question : The sum of the cubes of two given numbers is 10234, while the sum of the two given numbers is 34. What is the positive difference between the cubes of the two given numbers?

Option 1: 3484

Option 2: 3488

Option 3: 3356

Option 4: 8602


Team Careers360 20th Jan, 2024
Answer (1)
Team Careers360 22nd Jan, 2024

Correct Answer: 3484


Solution : $(a + b)^3= a^3+ b^3+ 3ab(a + b)$
$⇒(34)^3=10234+3ab(34)$
$⇒39304−10234 = 3ab(34)$
$⇒29070 = 102\times ab$
$⇒ab = \frac{29070}{102} = 285$
We know, $(a - b)^2= (a + b)^2 - 4ab$
$⇒(a - b)^2= 34^2 - 4 \times (285)$
$⇒(a - b)^2= 1156 -1140 = 16$
$⇒(a - b) = 4$ ........ (i)
Now $(a+b) = 34$ ........(i)
Solving both the equations (i) and (ii) we get,
$a = 19$ and $b = 15$
So, $a^3-b^3 = 19^3 - 15^3 = 3484$
Hence, the correct answer is 3484.

How to crack SSC CHSL

Candidates can download this e-book to give a boost to thier preparation.

Download Now

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