(In reply to re(7): Solution?
I don't like the x=-4 solution either, I only mentioned it because you were looking for other x values that would satisfy the equation for some fixed n. But I think it is perfectly reasonable to say sqrt(64) is -8. In other words, would you say x=-4 is one of the roots of:
f_2: x^4 - 4x^2 - 192 = 0
f_3: x^8 - 8x^6 + 16x^4 - 576x^2 - 27648 = 0
..,? If you consider these non-recursive cases of the problem then x=-4 is certainly a solution.
I don't like x=-4 as a solution because:
a) it doesn't hold for f_0(x), and
b) if you assume f_n(x) = -8, then f_n+1(x) is unsolvable.
Posted by tomarken
on 2006-11-20 01:26:34