# solve() is not giving the right solutions

Hey there,

i need your help on this one. The following sage code is giving me a headache:

- f(x) = x^3 + x^2 - 0.1
- solve(f==0, x)
- -->
- [x == -1/2
*(1/180*I*sqrt(13)*sqrt(3) + 7/540)^(1/3)*(I*sqrt(3) + 1) - 1/18*(-I*sqrt(3) + 1)/(1/180*I*sqrt(13)*sqrt(3) + 7/540)^(1/3) - 1/3, x == -1/2*(1/180*I*sqrt(13)*sqrt(3) + 7/540)^(1/3)*(-I*sqrt(3) + 1) - 1/18*(I*sqrt(3) + 1)/(1/180*I*sqrt(13)*sqrt(3) + 7/540)^(1/3) - 1/3, x == (1/180*I*sqrt(13)*sqrt(3) + 7/540)^(1/3) + 1/9/(1/180*I*sqrt(13)*sqrt(3) + 7/540)^(1/3) - 1/3]

So i'm getting these 3 solutions, but they are not in R (real numbers), which they should be. Im figuring there is some problem with really long terms or something? Is there an easy solution for this? Is the solve()-method here working as intended?

Regards, Ben

See casus irreducibilis...

You

canget "ostensibly real" solutions by expressing the quantities in trigonometric form. For example :