solving radical equations with parameters
I would like to find the solutions y to this type of equations: (1+x−√(1+x)2−4y)2=z with conditions on x,y,z (like 0<y<x≤18 and 0<z<x2).
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=14((1+x)2−(1+x−√z)2).
I also tried the same after specifying the conditions with assume()
, without success.