MATLAB: Cannot find ALL solutions to simultaneous equation

equationMATLABpolynomialsolvesymbolicvpasolve

Hi everyone, I would like to find ALL the solutions to this series of equations. Here is my code.
My problem is that it prompts me to use vpasolve, which doesn't give ALL the solutions. I tried "ReturnCondition", but to no avail.
My code is here:
clear all
syms x y z
eq1 = exp(x^2 + y^2 + z^2) == 9;
eq2 = x + x*y - z == 1;
eq3 = x + y + z == 1;
[solx,soly,solz] = solve([eq1,eq2,eq3],[x y z])

Best Answer

Hi CZ
If
exp(x^2+y^2+z^2) = 9
then
x^2+y^2+z^2 = log(9)
which is a lot less challenging for symbolic evaluation.
clear all
syms x y z C
eq1 = x^2 + y^2 + z^2 == C;
eq2 = x + x*y - z == 1;
eq3 = x + y + z == 1;
[solx,soly,solz] = solve([eq1,eq2,eq3],[x y z])
solz = 
 root(z1^4 - 5*z1^3 - z1^2*(C - 7) + z1*((5*C)/2 - 1/2) - C/2 + C^2/4 + 1/4, z1, 1)
 root(z1^4 - 5*z1^3 - z1^2*(C - 7) + z1*((5*C)/2 - 1/2) - C/2 + C^2/4 + 1/4, z1, 2)
 root(z1^4 - 5*z1^3 - z1^2*(C - 7) + z1*((5*C)/2 - 1/2) - C/2 + C^2/4 + 1/4, z1, 3)
 root(z1^4 - 5*z1^3 - z1^2*(C - 7) + z1*((5*C)/2 - 1/2) - C/2 + C^2/4 + 1/4, z1, 4)
There are expressions that are twice as long for x and y. You can get numerical results by plugging in log(9) for C and using the roots function to get four solutions. I wish I knew how to get the coefficients in solx, soly and solz into the roots function in a convenient way, but I don't.
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