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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re: Oops! Solution by reading the problem.

| Comment 3 of 5 |

(In reply to Oops! Solution by reading the problem. by Steve Herman)

actually it has several imaginary solutions a couple simple ones are N=+-i.

Using a computer algebra system there are 3 real and 20 complex solutions with N=0 having multiplicity of 3. Which makes sense because when the equation is expanded you end up with a 25 degree polynomial.

Posted by Daniel on 2009-04-05 17:54:38

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