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Math Help - problem solving for algebra

  1. #1
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    problem solving for algebra [solved]

    Good day everyone,

    Does anyone know how to solve this,

    Given 2^{2x}+64(2^{-x})= 32. Find the value of x.

    Thanks in advance!
    Last edited by imforumer; June 22nd 2008 at 05:10 AM. Reason: -
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  2. #2
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    Quote Originally Posted by imforumer View Post
    Given 2^{2x}+64(2^{-x})= 32. Find the value of x.
    Welcome to the forum Imforumer

    This first question multiply through the equation by 2^x

    2^{3x}- 32 \cdot 2^{x}+64=0

    let 2^x = u

    u^3 - 32 u+64=0

    Notice that u = 4 is a solution to this equation.

    Can you finish ?

    Bobak
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  3. #3
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    I also can't solve it, I stuck at where you stuck.

    Btw, the answer given is x=1.31(3 significant figure), x=2, no solution is provided =.="

    thanks bobak for your time.
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  4. #4
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    Quote Originally Posted by imforumer View Post
    I also can't solve it, I stuck at where you stuck.

    Btw, the answer given is x=1.31(3 significant figure), x=2, no solution is provided =.="

    thanks bobak for your time.
    If 4 is a root, then u-4 is a factor of u^3 - 32u + 64.So do polynomial devision and find the quotient.

    u^3 - 32u + 64 = (u-4)(u^2 + 4u - 16) = 0

    Surely you should know how to solve the quadratic u^2 + 4u - 16 = 0
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