perplexus.info :: Just Math : Fifth root (cubic) = Cube root (quintic)

Fifth root (cubic) = Cube root (quintic) (Posted on 2009-04-05)

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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Oops! Solution by reading the problem.

| Comment 2 of 5 |

Oops! The problem specifies that both sides of the equation must be positive. In that case, only one of the three values of N that satisfy the equation also satisfy the problem statement.

That's too bad, because the negative solution was my favorite.

By the way, the equation has no imaginary solutions.

Posted by Steve Herman on 2009-04-05 14:54:58

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