# Get solutions to multiple equations

williamkrill1 shared this question 3 years ago

Hi,

I have a list of cubic equations, say {x^3 + 2x + 3 = 1, x^3 + 2x + 3 = 4, x^3 + 2x + 3 = 9} and I would like to get the union of the solutions of these, but not the simultaneous solutions. In other words, I want a list of x-coordinates of the intersection points of the cubic y = x^3 + 2x + 3 and the lines y = 1, y = 4 and y = 9. The Solve command can handle multiple equations but solves them as a single system of equations, which in this case doe not yield a single solution.

Here is what i have so far: https://www.geogebra.org/m/fczha3gpUnfortunately the intersection tool cannot handle the red lines obtained by the set of equations.

Does anyone have a suggestions?

Thanks a lot for your help.

William try Zip({Root(x³ + 2x + 3 - k)}, k, {1, 4, 9}) 2

try Zip({Root(x³ + 2x + 3 - k)}, k, {1, 4, 9}) 1

Thank you! This worked with a slight modification:

x(Flatten(Zip({Root(x³ + 2x + 3 - k)}, k, {1, 4, 9}))) 