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Math Help - Quadratic equations????? PART-2

  1. #1
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    Quadratic equations????? PART-2

    well, here's another tough one, please explain the steps ...
    4(x 1/x) + 8(x + 1/x) 29 = 0

    [Ans: x=1/2, (- 9 √65)/ 4]
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  2. #2
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    Quote Originally Posted by ice_syncer View Post
    well, here's another tough one, please explain the steps ...
    4(x 1/x) + 8(x + 1/x) 29 = 0

    [Ans: x=1/2, (- 9 √65)/ 4]
    Its a nested quadratic :P

    To see that more clearly First write \left(x - \frac1{x}\right)^2 = \left(x + \frac1{x}\right)^2 - 4

    So

    4(x 1/x) + 8(x + 1/x) 29 = 4((x + 1/x) - 4) + 8(x + 1/x) 29 = 4(x + 1/x) + 8(x + 1/x) 45 = 0

    Now the last equation is a quadratic in (x+1/x). So solve it. Once you get a couple of answers for that solve the equation "x+1/x = previous answer", which is another quadratic.
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  3. #3
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    Quote Originally Posted by Isomorphism View Post
    Its a nested quadratic :P

    To see that more clearly First write \left(x - \frac1{x}\right)^2 = \left(x + \frac1{x}\right)^2 - 4

    So

    4(x 1/x) + 8(x + 1/x) 29 = 4((x + 1/x) - 4) + 8(x + 1/x) 29 = 4(x + 1/x) + 8(x + 1/x) 45 = 0

    Now the last equation is a quadratic in (x+1/x). So solve it. Once you get a couple of answers for that solve the equation "x+1/x = previous answer", which is another quadratic.
    You mean equating x+1/x to "a" or "be" or "BLABLA"? Thanks alot man,helped me alot!!
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