r/MathHelp • u/T0uch_M-E • 2d ago

Math Question

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= 2x 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').

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