Solve an equation with 3 variables

I have an equation with three variables, so I will have infinite^2 solutions. Is there a way Matlab can show the solutions set given some constraints on the variables?

The equation is: G = 1.5(X-X^2) + (Y-Y^2) + 0.5(Z-Z^2) - 2*XY - Z(X+Y)/ 2N(1 - 0.75X - 0.5Y - 0.25Z),

where N & G are known and X,Y,Z lie in (0,1).

Is there any way to see the integer solutions of this equation?

Thank you very much for your help!

Answer 1

[Torsten]

https://de.mathworks.com/help/matlab/ref/fimplicit3.html

Best wishes

Torsten.

[martina testori]

Thank you very much, Torsten.

Is there any way to access the values, so that I can find some numerical solutions?

Also, is there a solver for a 4 variables equations?

[Torsten]

Fix values for G,N,X and Y and use "fzero" to calculate the corresponding Z from the function

fun=@(Z) 1.5*(X-X.^2) + (Y-Y.^2) + 0.5*(Z-Z.^2) - 2*X.*Y - Z.*(X+Y)./ (2*N*(1 - 0.75*X - 0.5*Y - 0.25*Z))-G;

Best wishes

Torsten.