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Aaaaaaaa little late here, but A and A_A (read as A sub A, meaning the Ath term in the series or sequence A) can, technically, be any value. We also have the tetration of A by A, which means making a power tower (A^(A^A^A)) of A to the power of A — A times. Without assigning a value to A, or A_A, it isn't really possible to do any meaningful algebra to this to simplify it. If you pick an arbitrary value for one of them, it should be possible to determine the value of the other.

For example, let's say A = 1 and A_A = a (for clarity)

You end up with, after minimal algebra, 1 = (2a)/(sqrt(a)-1) - a

The result of this turns out to be extremely complicated, and I doubt there are many other good choices since 1 is generally the simplest case other than 0 and this equation gets several versions of undefined terms with A = 0, such as 0/0, 0^0, and 0 tetrated by 0 (which is just 0^0 0 times).

If you set A_A to be equal to 0, you get A = 0, which is boring, and if you set A_A to anything else, I don't even know how to begin solving ^(A)A in isolation, let alone multiplied by a complicated fraction with exponential functions in both the numerator and denominator.

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