Find a rational value of **k** such that there are four nonzero rational roots to the equation

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Find a rational value of **k** such that there are four nonzero rational roots to the equation

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For k =12: (x^3+12x)^(1/5) = (x^5-12x)^(1/3) has a solution for x =2.

For k =72: (x^3+72x)^(1/5 )= (x^5-72x)^(1/3) has a solution for x =3.

For k = 240: (x^3+240x)^(1/5 )= (x^5-240x)^(1/3) has a solution for x =4.

For k = 600: (x^3+600x)^(1/5) = (x^5-600x)^(1/3) has a solution for x =5.

So for every k = (x-1)*(x+1)*x^2 it has a unique solution.

pipo

Oops, misread. I see I had to find four nonzero roots for a certain k. More complicated then I thought.

pipo