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Math Help - Indicies and Substitution

  1. #1
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    Indicies and Substitution

    please help

    if you take y=x^1/3, find the values of x, if x^1/3 - 2x^-1/3= 1
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    x^{1/3} - 2x^{-1/3}= 1
    x^{1/3} - \frac{2}{x^{1/3}}= 1
    x^{2/3} - x^{1/3} - 2= 0
    This is a quadratic
    x^{1/3} = \frac{1 \pm \sqrt{1 - 4 \cdot 1 \cdot -2}}{2 \cdot 1}
    x^{1/3} = \frac{1 \pm 3}{2}
    x = (\frac{1 \pm 3}{2})^3
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  3. #3
    A riddle wrapped in an enigma
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    Quote Originally Posted by will_akrigg View Post
    please help

    if you take y=x^1/3, find the values of x, if x^1/3 - 2x^-1/3= 1
    y=x^{\frac{1}{3}}

    x^{\frac{1}{3}}-2x^{-\frac{1}{3}}=1

    Substituting,

    y-\frac{2}{y}=1

    y^2-2=y

    y^2-y-2=0

    (y-2)(y+1)

    y=2 \ \ or \ \ y=-1

    Substituting back into y=x^{\frac{1}{3}}, we get

    x^{\frac{1}{3}}=2

    \boxed{x=8}

    x^{\frac{1}{3}}=-1

    \boxed{x=-1}
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