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Math Help - Reducible Equations

  1. #1
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    Reducible Equations

    Solve:

    a) 4^{2x}- 5 .4 ^x +4 =0

    I know I have to make  u = 4x or something along those lines.

    But I have no idea what to do next


    Also,

    Find the value of A, B, C if A(x+1)^2 + Bx+C \equiv 2x^2 + 8x -6

    So I expand the first one...

     A(x^2+2x+1)+Bx+C

    then

     Ax^2 + 2Ax + A + Bx + C

     Ax^2 + x(2A+B)+A+C

    With this I know that A = 2 B = -4 but I can't figure out C. I get -2 but it's wrong. What did I do wrong?
    Last edited by jgv115; July 14th 2010 at 01:23 AM.
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  2. #2
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    a) You actually let u = 4^x so that you get a quadratic equation in u

    u^2 - 5u + 4 = 0.

    Solve it for u, then solve for x.


    b) A + C = -6 and you know A = 2. Solve for C. I think you'll also find that B = 4, not -4.
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  3. #3
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    Oh I thought 5.4^{x} meant \left(\dfrac{54}{10}\right)^x... I think it would be better to use \cdot to avoid confusion, as in 5\cdot4^x.
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  4. #4
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    Quote Originally Posted by undefined View Post
    Oh I thought 5.4^{x} meant \left(\dfrac{54}{10}\right)^x... I think it would be better to use \cdot to avoid confusion, as in 5\cdot4^x.
    Or brackets, i.e. 5\left(4^x\right).
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  5. #5
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    ok, I get it now!

     2+ C = -6

    So  C = -8

    Here is another (sorry I'm trying to pick this up myself with only the textbook and I'm trying my best )

    Find the value of A,B,C if Ax(x-1)+Bx^2+C(x-1)\equiv x-4-3x^2

    Expand:  Ax^2 - Ax+Bx^2+Cx-C

    I'm so sure what to do next so I group the terms into groups?

     x^2(A+B) -x(A-C) -C

    I'm pretty sure this is incorrect. Could someone help me out (not necessarily give me the answer)

    Thanks for all the help!!!!
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  6. #6
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    Quote Originally Posted by jgv115 View Post
    ok, I get it now!

     2+ C = -6

    So  C = -8

    Here is another (sorry I'm trying to pick this up myself with only the textbook and I'm trying my best )

    Find the value of A,B,C if Ax(x-1)+Bx^2+C(x-1)\equiv x-4-3x^2

    Expand:  Ax^2 - Ax+Bx^2+Cx-C

    I'm so sure what to do next so I group the terms into groups?

     x^2(A+B) -x(A-C) -C

    I'm pretty sure this is incorrect. Could someone help me out (not necessarily give me the answer)

    Thanks for all the help!!!!
    Technically what you have is right, but it's better to write it as

    (A + B)x^2 + (C-A)x - C \equiv -3x^2 + x - 4.

    That means

    A + B = -3
    C - A = 1
    -C = -4.

    Solve for A, B, C.
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  7. #7
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    Thanks!! I finally get it!!!

    I appreciate your help so much!! Thanks!!!!!!!!
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