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Math Help - Finding unknown constants

  1. #1
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    Finding unknown constants

    The question

    Find the constants A, B and C for:

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

    My attempt
    I tried to isolate the constants by substituting strategic values of x. For example:

    Let x = -1,
    C = -2

    Let x = 1,
    A = 1

    However, I cannot isolate B. I'm sure this question is trivial and my brain is still in holiday mode. Any assistance would be most welcome.
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  2. #2
    Super Member Random Variable's Avatar
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    You can expand the stuff on the right and then equate like terms. You'll get a system of equations.
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  3. #3
    MHF Contributor FernandoRevilla's Avatar
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    Quote Originally Posted by Glitch View Post
    Let x = -1, C = -2 Let x = 1, A = 1
    Right. Now, substitute (for example) x=0 and find B .


    Fernando Revilla
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  4. #4
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    Put x = 0 and use the values of A and C which you have already found to get B.
    Zero is just convenient - any constant apart from those which you have used will do.

    EDIT: Oops! Ah, well! I'm too slow, I guess.
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  5. #5
    Super Member Random Variable's Avatar
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    Or you could take the derivative of both sides and get  2x = 2A(x+1) + B(x+1) + B(x-1) + C , substitute x = -1, and see that  C = 0 .
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  6. #6
    MHF Contributor FernandoRevilla's Avatar
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    Quote Originally Posted by TheCoffeeMachine View Post
    EDIT: Oops! Ah, well! I'm too slow, I guess.
    Welcome to the Club.


    Fernando Revilla
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  7. #7
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    Thanks. This thread is proof that obvious things often dodge my thinking process!
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