# Solving radical inequalities

Can this be solved in Sage?

x-4>sqrt(x-2)

The standard solve method does not work, and neither does solve_ineq.

Solving radical inequalities

Can this be solved in Sage?

x-4>sqrt(x-2)

The standard solve method does not work, and neither does solve_ineq.

0

If you read the documentation for `solve_ineq`

you'll see that if you call `solve_ineq`

with an inequality as the argument, it's passed to Maxima assuming that it's a rational inequality (which this is certainly not). If you pass the inequality and variable as lists, Maxima is instructed to use the "Fourier elimination procedure" which can solve some general non-linear inequalities, but not this one unfortunately.

See "Case 1" and "Case 2" in the documentation for `solve_ineq`

.

Asked: **
2011-06-09 21:15:16 -0500
**

Seen: **406 times**

Last updated: **Jul 04 '11**

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.

I've been playing around with this question for a while now. I tried maxima's fourier elimination package with no success. I can't find a solution in Sage. Embarrassingly, WolframAlpha has no trouble: http://www.wolframalpha.com/input/?i=x-4+%3E+sqrt%28x-2%29

Yes, I noticed WA could solve it.

solve_ineq even fires an error here

If you read the documentation for `solve_ineq` you'll see that if you simply call `solve_ineq` with an inequality as the argument, it passed it to Maxima assuming that it's a rational inequality (which this is certainly not). If you pass the inequality and variable as lists then it passes them to Maxima using the fourier elimination procedure which can solve some general non-linear inequalities, but not this one unfortunately. See "Case 1" and "Case 2" in the documentation for `solve_ineq`.

Can you post your answer as an "answer" to "Can this be solved in Sage"?