A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • 5 years ago

the harmonic mean and geometric mean of two no. r in ratio 4:5. find ratio of those two no.????????

  • This Question is Closed
  1. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    i think i can work this out, but harmonic mean of two numbers is \[\frac{1}{\frac{1}{x}+\frac{1}{y}}\] and geometric mean is \[\sqrt{xy}\] and if the ratio is 4:5 we know \[4\sqrt{xy}=\frac{5}{\frac{1}{x}+\frac{1}{y}}\]

  2. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    \[\frac{5}{\frac{1}{x}+\frac{1}{y}}=\frac{5xy}{x+y}\] so we get \[4\sqrt{xy}=\frac{5xy}{x+y}\] now maybe square both sides to get \[16xy=\frac{25xy}{(x+y)^2}\] then ' \[\frac{16}{25}=\frac{1}{(x+y)^2}\] \[\frac{5}{4}=x+y\]

  3. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    probably a snappier way to do this.

  4. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    bt the ans wer given is 1/4

  5. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    @satellite: you forgot to square the term 5xy.

  6. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    And also the harmonic mean is 2/(1/x+1/y)

  7. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    So you get \[16xy=\frac{100x^2y^2}{(x+y)^2}\] \[16=\frac{100xy}{(x+y)^2}\] \[4x^2+4y^2-17xy=0\] \[4(y/x)^2-17(y/x)+4=0\] Which gives y/x=4 or 1/4

  8. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.