# Real Solution of x^3+8 == 0?

I do not understand the following:

```
sage: assume(x,'real')
sage: solve(x^3+8==0,x)
[]
```

Why does this equation have no solution? But -2 is a solution!

Thanks for help!

Real Solution of x^3+8 == 0?

I do not understand the following:

```
sage: assume(x,'real')
sage: solve(x^3+8==0,x)
[]
```

Why does this equation have no solution? But -2 is a solution!

Thanks for help!

add a comment

3

I think this is because `(-1)^(1/3)`

is not considered to be real.

```
sage: solve(x^3+1==0,x)
[x == 1/2*I*(-1)^(1/3)*sqrt(3) - 1/2*(-1)^(1/3), x == -1/2*I*(-1)^(1/3)*sqrt(3) - 1/2*(-1)^(1/3), x == (-1)^(1/3)]
sage: assume(x,'real')
sage: solve(x^3+1==0,x)
[]
```

Note that Maxima (which does our solving) doesn't actually care about `x`

being real, since it's a dummy variable.

```
(%i1) declare(x,real);
(%o1) done
(%i2) solve(x^3+1=0,x);
sqrt(3) %i - 1 sqrt(3) %i + 1
(%o2) [x = - --------------, x = --------------, x = - 1]
2 2
```

But when it's returned to Sage, somehow it doesn't keeps the `x=-1`

syntax and gets the cube root again, and it falls prey to

```
sage: (-1)^(1/3).n()
0.500000000000000 + 0.866025403784439*I
```

This is now http://trac.sagemath.org/sage_trac/ticket/11941.

1

An alternative approach is not to use the symbolic ring but a polynomial ring:

sage: x = polygen(RR)

sage: (x^3+8).roots()

[(-2.00000000000000, 1)]

This returns a list of roots in RR with multiplcities.

Asked: **
2011-10-18 08:07:48 -0500
**

Seen: **2,165 times**

Last updated: **Dec 11 '13**

Extended Euclid with polynomials

solve equation with double sum

How to make solve to use certain variables on the right side

Sage says equation isn't true while Mathematica says it is

Smallest positive numerical solution of an equation in one variable

Using the solution of equation

Copyright Sage, 2010. Some rights reserved under creative commons license. Content on this site is licensed under a Creative Commons Attribution Share Alike 3.0 license.