Question : The difference between the cubes of two given natural numbers is 6272, while the positive difference between the two given numbers is 8. What is the sum of the cubes of the two given numbers?
Option 1: 9728
Option 2: 9684
Option 3: 8000
Option 4: 9600

Question

Question : The difference between the cubes of two given natural numbers is 6272, while the positive difference between the two given numbers is 8. What is the sum of the cubes of the two given numbers?

Option 1: 9728

Option 2: 9684

Option 3: 8000

Option 4: 9600

Team Careers360 · Accepted Answer

Correct Answer: 9728

Solution : Given: $a^{3}–b^{3}=6272$ and $a–b=8$
We know that $(a–b)^{3}=a^{3}–b^{3}–3ab(a–b)$
Putting the given value, we have,
⇒ $(8)^{3}=6272–3ab(8)$
⇒ $24ab=6272–512$
⇒ $ab=\frac{5760}{24}=240$ ------------------------------------(1)
Putting the value of $a=b+8$ we have,
⇒ $(b+8)b=240$
⇒ $b^{2}+8b–240=0$
⇒ $b^{2}+20b–12b–240=0$
⇒ $b(b+20)–12(b+20)=0$
⇒ $(b+20)(b–12)=0$
⇒ $b=12,–20$
The value of a natural number can't be negative.
Putting the value of $b=12$ we have,
$a=20$
Now, we find, $a^{3}+b^{3}=20^{3}+12^{3}$
⇒ $a^{3}+b^{3}=8000+1728$
⇒ $a^{3}+b^{3}=9728$
Hence, the correct answer is 9728.

Exams

Colleges

Predictors

Resources

Quick links

Exams

Colleges & Courses

Predictors

Resources

Exams

Colleges

Predictors & E-Books

Resources

Engineering Preparation

Medical Preparation

Law Preparation

MBA Preparation

Exams

Colleges

Resources

Exams

Colleges

Predictors & Articles

Resources

Exams

Colleges

Predictors

Resources

Exams

Colleges

Upcoming Events

Resources

Exams

Colleges

Resources

Quick Links

Top Streams

Specializations

Resources

Top Providers

Exams

Colleges

Resources

Diploma Colleges

Exams

Colleges

Resources

Exams

Resources

Top Courses & Careers

Colleges

Exams

Upcoming Events

Resources

Other Exams

Exams

Colleges

Top Countries

Resources

Exams

Top Schools

Products & Resources

NCERT Study Material

Question : The difference between the cubes of two given natural numbers is 6272, while the positive difference between the two given numbers is 8. What is the sum of the cubes of the two given numbers?Option 1: 9728Option 2: 9684Option 3: 8000Option 4: 9600

Related Questions

Know More about

Upcoming Exams

Trending Articles around SSC CGL

Download the Careers360 App on your Android phone

Sign In/Sign Up

Question : The difference between the cubes of two given natural numbers is 6272, while the positive difference between the two given numbers is 8. What is the sum of the cubes of the two given numbers?
Option 1: 9728
Option 2: 9684
Option 3: 8000
Option 4: 9600