solve the following nonlinear algebraic equations simultaneously 3x^3 + x^2 -1 = 0 x^4 - 10*x^2 + 2 = 0 in matlab

To solve the given system of nonlinear equations simultaneously in MATLAB, you can use the "fsolve" function. Here's how you can do it:

main.m
% Define the equations as function handles
eqn1 = @(x) 3*x^3 + x^2 - 1;
eqn2 = @(x) x^4 - 10*x^2 + 2;

% Define a function that returns the vector of equations
eqns = @(x) [eqn1(x); eqn2(x)];

% Use fsolve to solve the system of equations
x0 = [0; 0]; % Initial guess for the solution
x = fsolve(eqns, x0);

% Display the solution
disp("Solution:")
disp(x)
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In this code, we first define the two equations as function handles eqn1 and eqn2, and then define a composite function eqns that returns the vector of equations. The x0 variable is the initial guess for the solution.

Finally, we use the fsolve function to solve the system of equations. The fsolve function finds a root of the equations numerically. The result is stored in the x variable, which represents the solution to the system of equations.

Note: Depending on the initial guess and the complexity of the equations, fsolve may not always converge to a solution. In such cases, you may need to adjust the initial guess or consider using other numerical methods.