A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • one year ago

if x+1/x=7, what is x^3+1/x^2?

  • This Question is Open
  1. zepdrix
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    Is it \(\large\rm \frac{x+1}{x}=7\) or \(\large\rm x+\frac{1}{x}=7\) ?

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

    (x) + (1/x) = 7, the second one

  3. zepdrix
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    Fractions are bad. No bueno. So let's multiply through to get rid of the x in the denominator. Multiplying by x gives us:\[\large\rm x^2+1=7x\]Ok with that step? What should we do next, what do you think? :)

  4. zepdrix
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    There is probably a cool way to relate the first equation to the second one... but I'm not seeing it. So instead what we can do is.. simply solve for the value of x in the first equation, and plug that value into the second equation.

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

    I do not think that is the way my teacher would like for me to go about it. I have been staring at this problem for a good 35 minutes and I'm stumped.

  6. zepdrix
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    No? Hmm. Ok lemme make sure I'm understanding the second equation then, is it \(\large\rm x^3+\frac{1}{x^2}\) ?

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

    Yes it is.

  8. Mertsj
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    \[x+\frac{1}{x}=7\] \[x=7-\frac{1}{x}\] \[\frac{1}{x}=7-x\]

  9. zepdrix
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    I was thinking maybe we could do something like this:\[\large\rm x+\frac{1}{x}=7\]Then,\[\large\rm \left(x+\frac{1}{x}\right)^2=49\]and\[\large\rm x^2+\frac{1}{x}=47\]But that doesn't quite get us the third power :( Darn...

  10. zepdrix
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    Woops typo,\[\large\rm x^2+\frac{1}{x^2}=47\]

  11. Mertsj
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    \[x^3+\frac{1}{x^2}=(7-\frac{1}{x})^3+\frac{1}{(7-x)^2}\]

  12. freckles
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    hero had a good way on a previous post like this one something about squaring both sides and also cubing both sides of that one equation

  13. freckles
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    \[(x+\frac{1}{x})^2=7^2 \\ (x+\frac{1}{x})^3=7^3\] some expanding will be involved

  14. freckles
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    you will get values for both \[x^2+\frac{1}{x^2} \text{ and } x^3+\frac{1}{x^3} \\ \text{ then add those you get } \\ x^3+\frac{1}{x^2}+x^2+\frac{1}{x^3} \\ =x^3+\frac{1}{x^2}+\frac{1}{x}(x^3+\frac{1}{x^2}) \\ =(x^3+\frac{1}{x^2})(1+\frac{1}{x}) \\ \text{ so you have } \\ x^3+\frac{1}{x^2}+x^2+\frac{1}{x^3}=(x^3+\frac{1}{x^2})(1+\frac{1}{x}) \\ \text{ solving for } x^3+\frac{1}{x^2} \\ \text{ you have } \\ x^3+\frac{1}{x^2}=\frac{x^3+\frac{1}{x^2}+x^2+\frac{1}{x^3}}{1+\frac{1}{x}}\] and remember you found the numerator above from doing what hero suggested and then you are given the denominator

  15. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    seems like there is a more prosaic way of doing this

  16. freckles
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    you know what I think I want to re-express what I said just a bit: \[x^3+\frac{1}{x^2}=\frac{(x^3+\frac{1}{x^3})+(x^2+\frac{1}{x^2})}{1+\frac{1}{x}}\] just wanted to group together what we actually will find from the above equations that I mentioned (or I mean hero had mentioned in a previous post)

  17. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    first equation tells you \[x=\frac{7\pm3\sqrt{5}}{2}\] it is much less fun, but i am sure will get an answer

  18. 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.