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Homework Help: Sum of All Real 'x'

  1. Apr 1, 2008 #1
    1. The problem statement, all variables and given/known data

    Find the sum of all real x such that

    ((2^x)-4)^3 + ((4^x)-2)^3=((4^x)+(2^3)-6)^3


    2. Relevant equations
    Nil



    3. The attempt at a solution

    (a-b)^3+3ab(a-b)=a^3-b^3

    This equation doesnt help as the LHS is a sum of two cubes.

    Is it wise to convert all fours and sixes as multiples of 2???

    Please help me to get a start at least.
     
  2. jcsd
  3. Apr 1, 2008 #2

    HallsofIvy

    User Avatar
    Science Advisor

    It is also true that a^3+ b^3= (a+ b)(a^2- ab+ b^2).
     
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