ASKSAGE: Sage Q&A Forum - RSS feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Sun, 11 Oct 2020 21:39:24 +0200plotted real intersection but solve only shows imaginaryhttps://ask.sagemath.org/question/53835/plotted-real-intersection-but-solve-only-shows-imaginary/I plotted `x^3 - x` and its derivative `3*x^2 - 1` to get two intersections in the real plane.
plot([x^3-x,3*x^2 - 1],-3,3,color=['blue','green'],legend_label=["f","derivative"])
![intersection](/upfiles/16024461625093012.png)
However, when I solved the two with `solve(x^3-x == 3*x^2 - 1, x)`, all I get are imaginary values.
solve(x^3-x == 3x^2 - 1,x)
[x == -1/2*(1/9*I*sqrt(37)*sqrt(3) + 1)^(1/3)*(I*sqrt(3) + 1) - 2/3*(-I*sqrt(3) + 1)/(1/9*I*sqrt(37)*sqrt(3) + 1)^(1/3) + 1, x == -1/2*(1/9*I*sqrt(37)*sqrt(3) + 1)^(1/3)*(-I*sqrt(3) + 1) - 2/3*(I*sqrt(3) + 1)/(1/9*I*sqrt(37)*sqrt(3) + 1)^(1/3) + 1, x == (1/9*I*sqrt(37)*sqrt(3) + 1)^(1/3) + 4/3/(1/9*I*sqrt(37)*sqrt(3) + 1)^(1/3) + 1]
Shouldn't `solve` show me the two intersections or am I disastrously confused?cybervigilanteSun, 11 Oct 2020 21:39:24 +0200https://ask.sagemath.org/question/53835/