Solve the following system of non-linear equations

Solve the following system of non-linear equations:

xyz - x 2 + y 2 = 1.34

xy - z 2 = 0.09

ex - e y + z = 0.41

Use the initial values of (x0, y0, z0) = (0, -1, 0) and the termination criateria of 0.1% for the approximate error norm.

[Walter Roberson]

https://www.mathworks.com/matlabcentral/answers/6200-tutorial-how-to-ask-a-question-on-answers-and-get-a-fast-answer

[Walter Roberson]

Something tells me that x 2 is not x times 2, but is instead intended to be

Answer 1

[Cameron B]

syms x y z
eqn1 = x*y*z - x^2 +y^2 - 1.34;
eqn2 = x*y - z^2 - 0.09;
eqn3 = exp(x) - exp(y) + z - 0.41;
sol = vpasolve(eqn1,eqn2,eqn3,[x,y,z],[0,-1,0]);
disp(sol.x)
disp(sol.y)
disp(sol.z)

[Walter Roberson]

It seems likely to me that the question posed was a direct homework assignment, and you have just provided a complete solution without guiding the poster through learning the steps...

On the other hand, the bit about "termination criateria of 0.1% for the approximate error norm." tells me that the user was expected to write iterative numeric solutions, so your symbolic solution might not be all that useful for them.