Quantcast

A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

jiteshmeghwal9

  • 2 years ago

If \(\LARGE{x^2=\frac{1}{x^2}+1}\), then \(\LARGE{x^2+\frac{1}{x^2}=?}\)

  • This Question is Closed
  1. jiteshmeghwal9
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    @hartnn @ParthKohli @ajprincess plz help :)

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

    \[\dfrac{1}{x^2} = x^2 - 1 \ \ \ \ \]So,\[x^2 + x^2 - 1 = 2x^2 -1\]

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

    Should it be a number value?

  4. jiteshmeghwal9
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \[\Huge{\color{red}{Ans.-\sqrt{5}}}\]

  5. Yahoo!
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 3

    x^4 = x^2 + 1 x^4 - x^2 - 1 = 0 put y = x^2

  6. jiteshmeghwal9
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    wait..

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

    That's a quartic equation in \(x\). So multiply through \(x^2\).\[x^4 = x^2 + 1\]

  8. jiteshmeghwal9
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    from where do u gt x^4?

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

    I had typed a long explanation, but Yahoo! spilled the beans =P

  10. Yahoo!
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 3

    Solve the given Equation @jiteshmeghwal9 x^2 = 1 + 1/x^2

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

    \(x^2 = 1 + \dfrac{1}{x^2}\) is what you have. Multiply \(x^2\) to both sides.

  12. jiteshmeghwal9
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    x^4=x^2+1

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

    That...

  14. jiteshmeghwal9
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Oops sorry i misread it

  15. jiteshmeghwal9
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    AArgh.... I'm going to be crazy :(

  16. jiteshmeghwal9
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Sorry dudes but i'm nt getting the right thing :(

  17. jiteshmeghwal9
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Need help

  18. rahul91
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    x^4-x^2-1=0 put x^2=t t^2-t-1=0 solve it

  19. jiteshmeghwal9
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    using quadratic formula ?

  20. rahul91
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yep

  21. jiteshmeghwal9
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \[{1 \pm \sqrt{1+4}\over2}={1 \pm \sqrt{5}\over2}\]

  22. jiteshmeghwal9
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    No.. i'm nt getting answer

  23. rahul91
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    substitute for x^2 in the expression needed

  24. Yahoo!
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 3

    Hm..Hm...After Solving i got sqrt5

  25. jiteshmeghwal9
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    can anybody give me steps to the solution, i'm getting confused :((((

  26. rahul91
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    hey substitute x^2= (1-sqrt(5))/2 in the expression u get the answer -sqrt(5)

  27. jiteshmeghwal9
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    ok

  28. Yahoo!
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 3

    @jiteshmeghwal9 ..Can u Check...ur Solution

  29. Yahoo!
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 3

    Is it sqrt5 or -sqrt5

  30. Yahoo!
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 3

    x^2 + 1 / x^2 = (x^4 + 1) / x^2

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

    \[x^4 -x^2 - 1 = 0 \]We can let \(t = x^2\).\[t^2 - t - 1 = 0 \iff \boxed{t = \dfrac{1\pm \sqrt 5}{2}}{}\]

  32. Yahoo!
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 3

    x^4=x^2+1 (x^2+2) / x^2 = 1 + 2/x^2

  33. sirm3d
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \[x^2=1/x^2+1\\x^4=1+x^2\\x^4-x^2-1=0\]by quadratic formula,\[x^2=\frac{1\pm \sqrt{5}}{2}\]disregard \(\displaystyle x^2= \frac{1-\sqrt{5}}{2}\) since this is not a real number

  34. Yahoo!
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 3

    nw put the value of x^2

  35. jiteshmeghwal9
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    well \(\sqrt{5}=\pm\sqrt{5}\) but in my book it is only given \(\sqrt{5}\) as answer :)

  36. Yahoo!
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 3

    Lol....Then...Go By My method

  37. jiteshmeghwal9
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    ohh! k

  38. Yahoo!
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 3

    1 + 2/x^2 1 + 4 / (1 + sqrt5) (5 + sqrt5)/ (1 + sqrt5) rationalize... u will get (4 sqrt 5)/4 = sqrt5

  39. Yahoo!
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 3

    Nw u Got it...:)

  40. jiteshmeghwal9
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    A little doubt here, just last doubt

  41. Yahoo!
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 3

    Wat?@jiteshmeghwal9

  42. jiteshmeghwal9
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    (x^2+2) / x^2 = 1 + 2/x^2 how did u gt this ?

  43. sirm3d
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \[x^2=\frac{1+\sqrt 5}{2}\\\frac{1}{x^2}=\frac{2}{1+\sqrt 5}\cdot\frac{1-\sqrt 5}{1-\sqrt 5}=-\frac{1}{2}+\frac{\sqrt 5}{2}\\x^2+\frac{1}{x^2}=(1/2+\sqrt 5/2)+(-1/2+\sqrt 5/2)=\sqrt {5}\]

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

    \[\dfrac{x^2 + 2}{x^2} = \dfrac{x^2}{x^2} + \dfrac{2}{x^2}\cdots\]

  45. jiteshmeghwal9
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    I m just gt confused just like my bro @maheshmeghwal9 :(

  46. Yahoo!
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 3

    Oh...i just Did to make calculation easy....if u dont get it...Go My The method used by sirm

  47. jiteshmeghwal9
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Well...now i gt it, thanx all of u a lot :) Mainly @Yahoo! thanx buddy ;)

  48. Yahoo!
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 3

    Well..)) .welcome

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

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy

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.