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koli123able

Prove that x^4+x^2=1

  • one year ago
  • one year ago

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  1. gohangoku58
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    whats x ?

    • one year ago
  2. koli123able
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    variable :P

    • one year ago
  3. gohangoku58
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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.

    • one year ago
  4. gohangoku58
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    or do u need to solve for x ???

    • one year ago
  5. koli123able
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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

    • one year ago
  6. koli123able
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    just prove it to 1

    • one year ago
  7. koli123able
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    by means of anything

    • one year ago
  8. gohangoku58
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    good luck with that :)

    • one year ago
  9. koli123able
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    what?

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

    • one year ago
  11. sauravshakya
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    PROVE ???

    • one year ago
  12. zostale
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    x= 1 :P

    • one year ago
  13. gohangoku58
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    nopes, x not =1 :P

    • one year ago
  14. zostale
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    then x= -1 :P

    • one year ago
  15. gohangoku58
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    nopes, x not =-1 :P

    • one year ago
  16. zostale
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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

    • one year ago
  17. gohangoku58
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    are u solving that for x ,saura ?

    • one year ago
  18. zostale
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    there you go ^^

    • one year ago
  19. gohangoku58
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    u copied that ^

    • one year ago
  20. zostale
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    yeah should i give the source ? :P

    • one year ago
  21. koli123able
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    it is equal to 1

    • one year ago
  22. gohangoku58
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    take a screenshot of your question

    • one year ago
  23. sauravshakya
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    |dw:1353238271333:dw|Looks like no solution

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

    • one year ago
  26. koli123able
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    Let x^2=y

    • one year ago
  27. koli123able
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    y^2+y

    • one year ago
  28. gohangoku58
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    thats a good substitution to solve for x

    • one year ago
  29. gohangoku58
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    u get quadratic in y

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

    • one year ago
  31. sauravshakya
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    |dw:1353238651184:dw||

    • one year ago
  32. gohangoku58
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    |dw:1353238684199:dw|

    • one year ago
  33. sauravshakya
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    |dw:1353238793125:dw| So, only two real roots

    • one year ago
  34. gohangoku58
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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

    • one year ago
  35. koli123able
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    how it is equal to 1??

    • one year ago
  36. koli123able
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    @gohangoku58

    • one year ago
  37. gohangoku58
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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.

    • one year ago
  38. koli123able
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    ginding??

    • one year ago
  39. gohangoku58
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    *finding

    • one year ago
  40. gohangoku58
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    :P

    • one year ago
  41. koli123able
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    ok

    • one year ago
  42. gohangoku58
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    *values

    • one year ago
  43. koli123able
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    PROVED!!!!

    • one year ago
  44. gohangoku58
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    what ?

    • one year ago
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