Presumably In[488] was intended to relate to the expression at 1:53 in the video; but I have to confess failure to establish any actual correspondence! Incidentally, I recall that the formula is practicably applicable only when there is a single real root. WFL On 3/10/20, Bill Gosper <billgosper@gmail.com> wrote:
https://www.youtube.com/watch?v=N-KXStupwsc offers an attractive expression for (one) solution of the general cubic, but I can't make it work. Have I entered this incorrectly? In[488]:= Power[#1 - Sqrt[#1^2 + #2^3], (3)^-1] + Power[#1 + Sqrt[#1^2 + #2^3], (3)^-1] - b/3/a &[-b^3/27/a^3 + b c/6/a/a - d/2/a, c/3/a - b^2/9/a/a]
Out[488]= -(b/(3 a)) + (-(b^3/(27 a^3)) + (b c)/(6 a^2) - d/(2 a) - Sqrt[(-(b^2/(9 a^2)) + c/(3 a))^3 + (-(b^3/(27 a^3)) + (b c)/( 6 a^2) - d/(2 a))^2])^( 1/3) + (-(b^3/(27 a^3)) + (b c)/(6 a^2) - d/(2 a) + Sqrt[(-(b^2/(9 a^2)) + c/(3 a))^3 + (-(b^3/(27 a^3)) + (b c)/( 6 a^2) - d/(2 a))^2])^(1/3) —rwg _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun