How I can solve a simple system of equations

Hi,

I want to solve the following system

w = A*(1-gamma)*k^(gamma);
r = A * gamma * k^(gamma-1);
H = w + (1-beta)*(1+r)*(k+debt)-(r-n)*debt;
k =(1/(1+n))*(mu*H) - debt; 

My parameters are defined as follows 

alpha = 0.6; 
beta = alpha; 
A = 7;
xi = 0 ; 
gamma = 0.3; 
debt = 0.05; % debt = 0.22; 
mu = (1-alpha)/(1-alpha*xi);
n = 1.097;

Basically, everything boils down to a polynomial expression for k,

could you please advice how this can be solved in the most efficient way ?

PS: All are scalars if it matters, and apparently the solution for k might be multiple and not necessary real

Many thanks

Answer 1

[David Sanchez]

Define k as symbolic

syms k
alpha = 0.6; 
beta = alpha; 
A = 7;
xi = 0 ; 
gamma = 0.3; 
debt = 0.05; % debt = 0.22; 
mu = (1-alpha)/(1-alpha*xi);
n = 1.097;

w = A*(1-gamma)*k^(gamma);
r = A * gamma * k^(gamma-1);
H = w + (1-beta)*(1+r)*(k+debt)-(r-n)*debt;
k =(1/(1+n))*(mu*H) - debt;
>> k

k =

(400*(21/(25*k^(7/10)) + 2/5)*(k + 1/20))/2097 + (1960*k^(3/10))/2097 - 14/(699*k^(7/10)) - 8291/209700

[msh]

Thank you for the effort, the only problem is that i cannot get the solution for k. Is something else that i can do next ?