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Math Help - Need help with a specific method in reducing quadratic equations

  1. #1
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    Need help with a specific method in reducing quadratic equations

    Ok, so theoretically some equations can be treated as quadratic and we're supposed to solve by having u=b (the middle term) and multiply the middle term, and 'a,' by u.

    For example......

    x-[3*sqrt(x)]-4=0

    then replace x with u, and u equals sqrt(x)

    therefore.....u^2-3u-4=0

    then once factored you get u+1=0 with u=-1 and u-4=0 with u=4.

    and since we substitued sqrt(x) with u we square both -1 and 4 which means x= 1 or 16

    This I understand, but how do you do that method with a problem where the exponents are in fraction form? Like this one.....

    x^(1/2)-4x^(1/4)+2=0
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by some_nerdy_guy View Post
    Ok, so theoretically some equations can be treated as quadratic and we're supposed to solve by having u=b (the middle term) and multiply the middle term, and 'a,' by u.

    For example......

    x-[3*sqrt(x)]-4=0

    then replace x with u, and u equals sqrt(x)

    therefore.....u^2-3u-4=0

    then once factored you get u+1=0 with u=-1 and u-4=0 with u=4.

    and since we substitued sqrt(x) with u we square both -1 and 4 which means x= 1 or 16

    This I understand, but how do you do that method with a problem where the exponents are in fraction form? Like this one.....

    x^(1/2)-4x^(1/4)+2=0
    x^{\frac 12 } - 4 x^{ \frac 14} + 2 = \left( x^{ \frac 14 } \right)^2 - 4 \left( x^{ \frac 14} \right) + 2 = 0

    Let u = x^{\frac 14}
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  3. #3
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    Ok, I see it now. Thank-you.
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