Question

5.
The sum of all real x such that (2^x- 4)^3+(4^x – 2)^3 = (4^x+2^x-6)^3
is :​

Answer 1

Step-by-step explanation:

Express the RHS as ( (4^x - 2) + (2^x - 4) )^3

Expand as: (4^x - 2)^3 + (2^x - 4)^3 + 3(4^x - 2)^2(2^x - 4) + 3(4^x - 2)(2^x - 4)^2

Set this equal to the LHS and rearrange to get (4^x - 2)(2^x - 4)(4^x + 2^x - 6) = 0

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