The sum of two numbers is 6 times their | Class 11 Mathematics Chapter Sequence and Series, Sequence and Series NCERT Solutions

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Academic session 2026-27, Chapter 8 in the current curriculum.

Welcome to the NCERT Solutions for Class 11 Mathematics - Chapter Sequence and Series. This page offers a step-by-step solution to the specific question from Exercise 3, Question 28:

The sum of two numbers is 6 times their geometric mean, show that numbers are in the ratio open parentheses 3 space plus space 2 square root of 2 close parentheses space : space open parentheses 3 minus 2 square root of 2 close parentheses.

. With detailed answers and explanations for each chapter, students can strengthen their understanding and prepare confidently for exams. Ideal for CBSE and other board students, this resource will simplify your study experience.

Question 28:

The sum of two numbers is 6 times their geometric mean, show that numbers are in the ratio open parentheses 3 space plus space 2 square root of 2 close parentheses space : space open parentheses 3 minus 2 square root of 2 close parentheses.

Answer:

Let the two numbers be a and b.

G.M. = square root of a b end root

According to the given condition,

a space plus space b space equals space 6 square root of a b end root space space space space space space space space space space space space space space space space space space space space space space space space... left parenthesis 1 right parenthesis rightwards double arrow open parentheses a space plus space b close parentheses squared space equals space 36 open parentheses a b close parentheses

Also,

open parentheses a minus b close parentheses squared space equals space open parentheses a plus b close parentheses squared space minus space 4 a b space equals space 36 a b space minus 4 a b space equals space 32 a b rightwards double arrow a minus b space equals space square root of 32 space square root of a b end root space equals space 4 space square root of 2 space square root of a b end root space space space space space space space space space space space space space space space space space space space space space space space space space... left parenthesis 2 right parenthesis

Adding (1) and (2), we obtain

2 a space equals space open parentheses 6 space plus space 4 square root of 2 close parentheses square root of a b end root rightwards double arrow a space equals space open parentheses 3 space plus space 2 square root of 2 close parentheses square root of a b end root

Substituting the value of a in (1), we obtain

b space equals space 6 square root of a b end root space minus space open parentheses 3 plus 2 square root of 2 close parentheses square root of a b end root rightwards double arrow b space equals space open parentheses 3 space minus space 2 square root of 2 close parentheses space square root of a b end root a over b space equals space fraction numerator open parentheses 3 space plus 2 square root of 2 close parentheses square root of a b end root over denominator open parentheses 3 minus 2 square root of 2 close parentheses square root of a b end root end fraction space equals fraction numerator 3 space plus space 2 square root of 2 over denominator 3 minus 2 square root of 2 end fraction space

Thus, the required ratio is open parentheses 3 space plus space 2 square root of 2 close parentheses space : space open parentheses 3 minus 2 square root of 2 close parentheses.

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Study Tips for Answering NCERT Questions:

NCERT questions are designed to test your understanding of the concepts and theories discussed in the chapter. Here are some tips to help you answer NCERT questions effectively:

  • Read the question carefully and focus on the core concept being asked.
  • Reference examples and data from the chapter when answering questions about Sequence and Series.
  • Review previous year question papers to get an idea of how such questions may be framed in exams.
  • Practice answering questions within the time limit to improve your speed and accuracy.
  • Discuss your answers with your teachers or peers to get feedback and improve your understanding.

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Comments

  • Subhajit paul
  • Oct 17, 2018

Thank you

  • Neetu
  • Aug 19, 2018

Not clear cut

  • Neetu
  • Aug 19, 2018

How did you get -4ab

  • Anjali
  • Jun 19, 2018

Thanks a lot for this solution. This solution is very helpful for me.😄

  • Venkatesh Naidu
  • Sep 23, 2017

Thank you sir/ma’am. May Krishna shower you with his blessings.

  • Dark shadow
  • Jul 14, 2017

Nice solition! Thanks a lot!

  • Sajad alam
  • Jul 13, 2017

How to get (a-b) part

  • deepak
  • Jun 21, 2017

Why we should not take two no. a and ar?

  • Navjot
  • Feb 08, 2017

Thank you very much. Very simple and easy method.

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Welcome to the NCERT Solutions for Class 11 Mathematics - Chapter . This page offers a step-by-step solution to the specific question from Excercise 3 , Question 28: The sum of two numbers is 6 times their geometric mean, show that numbers are in the ratio ....

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