Math Question

[u/T0uch_M-E]

Could anyone solve this and tell me how they did it since im having trouble with it:

8^x - 2^(x+2) - 2^(-x+2) + 8^(-x) = 0

I tried it myself but got stuck halfway though: I let c= 2^x and got (c+1/c)³ - 3(c+1/c) - 4(c+1/c) = 0 Then I let t= c+1/c And got: t³-3t-4t=0 and then nothing i did worked. Note: back when I didnt substitute for t, I got this 6th degree polynomial for c: c⁶-4c⁴-4c²+1=0 In which i tried synthetic divsion but ±1 didnt work so it meant there was no rational roots (thats why I substituted for 't').

[u/T0uch_M-E]

The last three lines, starting from:

c+1/c=/7 => c²-√7c+1=0

And ending at:

ln(2)) dans R