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Find Five Fractions (Posted on 2016-03-27) Difficulty: 4 of 5
There are already two puzzles on this site asking to find three real roots to an equation of the form:
(x^3+k*x)^(1/5) = (x^5-k*x)^(1/3)

The two puzzles are k=2 here and k=20 here.

I challenge you to find a rational value of k such that there are four nonzero rational roots to the equation above.

No Solution Yet Submitted by Brian Smith    
Rating: 4.0000 (2 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re: Heuristic approach - spoiler Comment 2 of 2 |
(In reply to Heuristic approach - spoiler by Harry)

Excellent!  Not just one rational k, but an infinite number of them!
  Posted by Steve Herman on 2016-03-28 07:27:33

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