Find all possible real number(s) N that satisfy this equation:

⁵√(N³ + 2N) = ³√(N⁵ - 2N)

where, the common value of both sides of the equation is positive.

It seems that the cross over from the left side being greater to the right side being greater (as N increases) is between N = 1.41 and 1.42 -- which leads to a guess that N is the square root of 2. Since there appears to be an increasing divergence, I suspect this is the only value of N which satisfies.  Rather "empirical arithmetic", n'est-ce pas?? (i.e. leave proof/derivation -- or refutation --to those who enjoy).

Posted by ed bottemiller on 2009-04-06 17:20:38