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Math Help - polynomial and rational function

  1. #1
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    polynomial and rational function

    By using the substitution y=x+1/x, find all the real roots of the equation (x^3) -4x+6-(4/x)+(1/x^3)



    y=x+1/x(1)
    y2=x2+(1/x^2)+2...(2)
    x2+(1/x^2)=y2-2
    x3-4x+6-4/x +(1/x^2) =0
    (x2+1/x^2 )(x+1/x)-(x+1/x)- 4(x+1/x)+6=0
    From(1)and(2), (y2-2)(y)-y-4y+6=0
    y3-7y+6=0
    ....
    what should I do now?
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  2. #2
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    Re: polynomial and rational function

    polynomial and rational function-14-jan-14.png
    Thanks from Trefoil2727
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  3. #3
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    Re: polynomial and rational function

    then solve it

    y=1, y=2 , y=-3 ...
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