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Math Help - Binomial Theorem problem

  1. #1
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    Binomial Theorem problem

    Hi, i have been trying to figure the below problem for ages, i can't figure it out, if someone could give me a lead that would very much appreciated

    In the expansion (a+2bx)^12, a and b are constants. The coefficient of is 3168, while that of x^12 is . Find the values of a and b.

    Thanks in advance
    kleyzam
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by kleyzam View Post
    Hi, i have been trying to figure the below problem for ages, i can't figure it out, if someone could give me a lead that would very much appreciated

    In the expansion (a+2bx)^12, a and b are constants. The coefficient of is 3168, while that of x^12 is . Find the values of a and b.

    Thanks in advance
    kleyzam
    The term with x^{12} is (2bx)^{12} , so:

    (2b)^{12}=\frac{1}{4096}

    (and you should recognise 4096 as 2^{12} )

    The term with x^5 is:

     <br />
{12 \choose 5}(2bx)^5a^7<br />

    so:

     <br />
{12 \choose 5}(2b)^5a^7=3168<br />

    CB
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  3. #3
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    I still can't figure out how to find the a and b
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  4. #4
    Grand Panjandrum
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    Quote Originally Posted by CaptainBlack View Post
    (2b)^{12}=\frac{1}{4096}

    (and you should recognise 4096 as 2^{12} )
    Quote Originally Posted by kleyzam View Post
    I still can't figure out how to find the a and b
    What have you done to try and solve the above equation for b?

    CB
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