ASKSAGE: Sage Q&A Forum - Latest question feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Tue, 25 Jun 2013 03:00:31 -0500solving radical equations with parametershttps://ask.sagemath.org/question/10277/solving-radical-equations-with-parameters/I would like to find the solutions $y$ to this type of equations: $$\left(1+x -\sqrt{(1+x)^2-4y}\right)^2=z$$
with conditions on $x,y,z$ (like $0\lt y\lt x\leq \frac18$ and $0\lt z\lt x^2$).
Using `solve` with the option `to_poly_solve`:
sage: solve((1+x - sqrt((1+x)^2-4*y))^2 == z, y, to_poly_solve=True)
[y == 1/2*x^2 - 1/2*(x + 1)*sqrt(x^2 + 2*x - 4*y + 1) + x - 1/4*z + 1/2]
does not seem to work because $y$ appears on the right side of the solution. I expect to find a solution like
$$y=\frac14\left((1+x)^2-\left(1+x-\sqrt{z}\right)^2\right).$$
I also tried the same after specifying the conditions with `assume()`, without success.nejimbanTue, 25 Jun 2013 03:00:31 -0500https://ask.sagemath.org/question/10277/