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Fifth root (cubic) = Cube root (quintic) (Posted on 2009-04-05) Difficulty: 3 of 5
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.

No Solution Yet Submitted by K Sengupta    
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split the difference? Comment 5 of 5 |
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
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