Please wait...
1800-212-7858 (Toll Free)
9:00am - 8:00pm IST all days

or

Thanks, You will receive a call shortly.
Customer Support

You are very important to us

For any content/service related issues please contact on this toll free number

022-62211530

Mon to Sat - 11 AM to 8 PM

begin mathsize 12px style If space straight a space equals space fraction numerator straight b space plus space straight c space over denominator 2 end fraction comma space straight c space equals space fraction numerator straight a space plus space straight b over denominator 2 end fraction space and space straight b space is space the space mean space proportional space between space straight a space and space straight c comma
prove space that space 1 over straight a space plus space 1 over straight c space equals space 2 over straight b end style

Asked by Topperlearning User 14th September 2017, 9:47 AM
Answered by Expert
Answer:

Given comma space straight a equals fraction numerator straight b plus straight c over denominator 2 end fraction space and space straight c equals fraction numerator straight a plus straight b over denominator 2 end fraction
Since space straight b space is space the space mean space proportional space between space straight a space and space straight c comma space we space have
straight b squared equals ac
rightwards double arrow straight b squared equals open parentheses fraction numerator straight b plus straight c over denominator 2 end fraction close parentheses open parentheses fraction numerator straight a plus straight b over denominator 2 end fraction close parentheses
rightwards double arrow 4 straight b squared equals ab plus straight b squared plus ac plus bc
rightwards double arrow 3 straight b squared equals ab plus bc plus ac
rightwards double arrow 3 left parenthesis ac right parenthesis equals ab plus bc plus ac
rightwards double arrow 2 ac equals ab plus bc
rightwards double arrow 2 over straight b equals 1 over straight c plus 1 over straight a space space space space space space space.... left parenthesis Dividing space both space the space sides space by space abc right parenthesis
rightwards double arrow 1 over straight a plus 1 over straight c equals 2 over straight b

Answered by Expert 14th September 2017, 11:47 AM
Rate this answer
  • 1
  • 2
  • 3
  • 4
  • 5
  • 6
  • 7
  • 8
  • 9
  • 10

You have rated this answer /10

Your answer has been posted successfully!