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parametric equations - how do I equate coefficients

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    I have the equation A(1+t^2) + (Bt+c)t =1

    How do I work out the value of A , B and C?
    Below is how I try working it out, what am i doing wrong?

    firstly, i multiply out the brackets so I get:
    A + At^2 + Bt^2 +ct

    I then collect constants and terms:
    A = 1
    At^2 + Bt^2 + tc = 0


    now what do i do / where did I go wrong?
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    (Original post by 2cool)
    I have the equation A(1+t^2) + (Bt+c)t


    This is not an equation?
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    (Original post by steve2005)
    This is not an equation?
    I got it from the original parametric equation:

    1/ t(1+t^2) = A/t + (Bt+c)/1+t^2
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    (Original post by 2cool)
    I have the equation A(1+t^2) + (Bt+c)t =1

    Sorry but is this an equation or an identity

    If it is an equation then you cannot equate coefficients



    Can you post the actual question?
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    (Original post by 2cool)
    I got it from the original parametric equation:

    1/ t(1+t^2) = A/t + (Bt+c)/1+t^2

    Do you mean




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    (Original post by 2cool)
    I got it from the original parametric equation:

    1/ t(1+t^2) = A/t + (Bt+c)/1+t^2
    Hang on

    Are you trying to do partial fractions?
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    In wich case

    1 = A(1+t^2) + t(Bt+C) = (A+B)t^2 + Ct + A

    Equating coefficients


    (A+B) = 0
    C = 0
    A = 1
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    (Original post by steve2005)
    Do you mean




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    i meant the first 1 , A sorry about my poor equation writing !

    (Original post by TenOfThem)
    Hang on

    Are you trying to do partial fractions?
    yes

    (Original post by TenOfThem)
    In wich case

    1 = A(1+t^2) + t(Bt+C) = (A+B)t^2 + Ct + A

    Equating coefficients


    (A+B) = 0
    C = 0
    A = 1

    why does A+B have to = 0 ?
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    (Original post by 2cool)
    why does A+B have to = 0 ?
    How many t^2 do you have on the LHS
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    (Original post by TenOfThem)
    How many t^2 do you have on the LHS
    one ....
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    (Original post by 2cool)
    one ....
    Where?

    1 = (A+B)t^2 + Ct + A
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    ahh there are 2, because multiplied out gets

    At^2 + Bt^2 right?
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    (Original post by 2cool)
    ahh there are 2, because multiplied out gets

    At^2 + Bt^2 right?
    No

    I will ask again

    How many t^2 do you have on the Left Hand Side
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    (Original post by TenOfThem)
    No

    I will ask again

    How many t^2 do you have on the Left Hand Side
    damn, talk about not reading th equestion,


    none, you have just the constant 1
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    none

    exactly

    so you also have none on the RHS

    that is why A+B = 0
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    ahhh yes thanks... however something im a bit confused about in my head, maybe this is a wrong explanation

    but

    x = x^2 if x = 1

    so wouldnt this mean that you dont have to have t^2 on both sides?

    edit: I think because you have a t^2 + Ct + A , this would be like x^2 = x + 1 which isnt solvable which answers my own question
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    When equating coefficients you have an IDENTITY not an EQUATION that means that it holds true for all values of t
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    (Original post by TenOfThem)
    When equating coefficients you have an IDENTITY not an EQUATION that means that it holds true for all values of t
    ahhh ! ! thank you very much for the help ! can only give one +rep !
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    (Original post by 2cool)
    ahhh ! ! thank you very much for the help ! can only give one +rep !
    No Problem
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    Y u no learn to latex

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