Hi, it seems that the inequality you provided does not have an explicit solution that can be obtained symbolically. Therefore, the solve function may not be able to find the solution.
In such cases, you can use numerical methods to approximate the solution. One approach is to use the fzero function to find the root of a function numerically. Here's an example of how you can apply it to your inequality:
syms z1 real
% Define the function to find the root of
f = @(z1) 2 - (3*z1 + (4 - 3*z1^2)^(1/2));
% Find the root numerically
z1 = fzero(f, [0 sqrt(4/3)]);
In this code, the function f represents the inequality 2 < 3*z1 + (4 - 3*z1^2)^(1/2). The fzero function is then used to find the value of z1 that satisfies this inequality within the specified range [0 sqrt(4/3)].
However, since the expression for lambda involves division by z1, which can be zero in this case, it is not possible to evaluate lambda for the obtained z1 value. We can try to plot this inequality with the following code :
syms z1 real
% Define the function to plot
f = 3*z1 + (4 - 3*z1^2)^(1/2);
% Plot the function
fplot(f, [-sqrt(4/3) sqrt(4/3)], 'LineWidth', 2);
hold on;
% Plot the horizontal line y = 2
yline(2, 'r--', 'LineWidth', 2);
% Set plot properties
title('Plot of 2 < 3*z1 + (4 - 3*z1^2)^(1/2)');
xlabel('z1');
ylabel('f(z1)');
legend('3*z1 + (4 - 3*z1^2)^(1/2)', 'y = 2');
grid on;
