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Math Help - Maths

  1. #1
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    Maths

    3X^3-16X-1 is identical to or congruent to Ax(x-1)(x+2)+B(x+1)^2+C(4x^2+3) What is the value of A,B and C. I know the answer what I need is the working out!
    Last edited by richardwilson; July 11th 2014 at 04:21 AM.
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  2. #2
    MHF Contributor ebaines's Avatar
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    Re: Maths

    If you multiply everything out and group terms you get:

    Ax^3 + (A+B+4C)x^2 +(-2A+2B)x +(B+3C) = 3x^3 -16x-1

    So there are four equations in three unknowns:

    a) A=3
    b)A+B+4C = 0
    c)-2A+2B = -16
    d)B+3C = -1

    From (a) you have A=3, then from (c) B=-5, then from (d) C=4/3. Finally, check that these values work in equation (b), but that gives 3-5+16/3 = 0, which is incorrect. So the answer is: there is no solution that works for all values of x. Are you sure you wrote the equation correctly?
    Thanks from topsquark
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  3. #3
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    Re: Maths

    Quote Originally Posted by richardwilson View Post
    3X^3-16X-1 is identical to or congruent to Ax(x-1)(x+2)+B(x-1)^2+C(4x^2+3) What is the value of A,B and C. I know the answer what I need is the working out!
    Thanks for your help.

    Regards Richard.
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