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.
