MATLAB: Solving an equation to get a particular solution

equation

Hello,
The following code was designed to solve a particular equation depending on a variable "n", which gives many solutions(both positive and negative) for each n. However, my objective is to get only positive solutions corresponding to each n. Would you let me know what command I should include to get such solutions?
format long e
T=0.1;
k=1.0;        
k_1=0.2;      
k_2=0.1;      
%k_2=[0.1:0.1:1.0];
a_p=0.0001;     
k_p=a_p/10;   
a_q=0.00015;   
k_q=0.00002;    
theta=0.01;               
m1=0.0000005;             
m2=0.0000002;            
W=0.00002;               
syms x
gamma=(a_p*k*k_2)/(k_p*m1*k_1);
for n=1:1:10
equation=[(1+sqrt(gamma*theta^n))/sqrt(gamma+sqrt(theta^n))]^2-[(theta+x)/(1+x)]^(n+1)==0;  
sol=solve(equation,x);   <======= Any additional command to get positive solutions? 
fprintf('%d\n',n);
fprintf('%.10e\n',sol);
end

Best Answer

Use vpasolve to get all the results, then in the second fprintf call, simply choose the values of ‘sol’ greater than zero to get only the positive solutions:
for n=1:1:10
    equation=[(1+sqrt(gamma*theta^n))/sqrt(gamma+sqrt(theta^n))]^2-[(theta+x)/(1+x)]^(n+1)==0;
    sol=vpasolve(equation,x);   % <======= Any additional command to get positive solutions?
    fprintf('%d\n',n);
    fprintf('%.10e\n',sol(sol > 0));
end
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