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koli123able

  • 2 years ago

Prove that x^4+x^2=1

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  1. gohangoku58
    • 2 years ago
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    whats x ?

  2. koli123able
    • 2 years ago
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    variable :P

  3. gohangoku58
    • 2 years ago
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    i mean is it cube root of unity ? or imaginary number i or something else ? if not, then u just said its variable, so x^4+x^2 can't equal 1.

  4. gohangoku58
    • 2 years ago
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    or do u need to solve for x ???

  5. koli123able
    • 2 years ago
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    I don't know that is what I am trying to figure out... this was the question in my paper and I left it blank

  6. koli123able
    • 2 years ago
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    just prove it to 1

  7. koli123able
    • 2 years ago
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    by means of anything

  8. gohangoku58
    • 2 years ago
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    good luck with that :)

  9. koli123able
    • 2 years ago
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    what?

  10. gohangoku58
    • 2 years ago
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    i think question is incomplete...we can solve for x, but can't prove that =1...

  11. sauravshakya
    • 2 years ago
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    PROVE ???

  12. zostale
    • 2 years ago
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    x= 1 :P

  13. gohangoku58
    • 2 years ago
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    nopes, x not =1 :P

  14. zostale
    • 2 years ago
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    then x= -1 :P

  15. gohangoku58
    • 2 years ago
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    nopes, x not =-1 :P

  16. zostale
    • 2 years ago
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    x^4 +x^2=1 => => x^4 +x^2 -1 = 0 => (x +0.786)*(x -0.786)*(x^2 +1.618) = 0 Real solutions: Root 1: -0.786 Root 2: 0.786 Complex roots: Root 3: 0+1.272 * i Root 4: 0-1.272 * i

  17. gohangoku58
    • 2 years ago
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    are u solving that for x ,saura ?

  18. zostale
    • 2 years ago
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    there you go ^^

  19. gohangoku58
    • 2 years ago
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    u copied that ^

  20. zostale
    • 2 years ago
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    yeah should i give the source ? :P

  21. koli123able
    • 2 years ago
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    it is equal to 1

  22. gohangoku58
    • 2 years ago
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    take a screenshot of your question

  23. sauravshakya
    • 2 years ago
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    |dw:1353238271333:dw|Looks like no solution

  24. zostale
    • 2 years ago
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    1 Attachment
  25. gohangoku58
    • 2 years ago
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    koli, any luck with screenshot ?

  26. koli123able
    • 2 years ago
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    Let x^2=y

  27. koli123able
    • 2 years ago
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    y^2+y

  28. gohangoku58
    • 2 years ago
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    thats a good substitution to solve for x

  29. gohangoku58
    • 2 years ago
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    u get quadratic in y

  30. sauravshakya
    • 2 years ago
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    x^4+x^2-1=0|dw:1353238509864:dw|

  31. sauravshakya
    • 2 years ago
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    |dw:1353238651184:dw||

  32. gohangoku58
    • 2 years ago
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    |dw:1353238684199:dw|

  33. sauravshakya
    • 2 years ago
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    |dw:1353238793125:dw| So, only two real roots

  34. gohangoku58
    • 2 years ago
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    so for any of the 4 values of x we found above, u can prove that x^4+x^2= 1

  35. koli123able
    • 2 years ago
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    how it is equal to 1??

  36. koli123able
    • 2 years ago
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    @gohangoku58

  37. gohangoku58
    • 2 years ago
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    solving for x in x^4+x^2=1 means ginding vales of x for which x^4+x^2 equals 1 so, for the 4 values we found, x^4+x^2 will equal 1.

  38. koli123able
    • 2 years ago
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    ginding??

  39. gohangoku58
    • 2 years ago
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    *finding

  40. gohangoku58
    • 2 years ago
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    :P

  41. koli123able
    • 2 years ago
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    ok

  42. gohangoku58
    • 2 years ago
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    *values

  43. koli123able
    • 2 years ago
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    PROVED!!!!

  44. gohangoku58
    • 2 years ago
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    what ?

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