issue to resolve equation

Hi,

I have an exercise on Matlab and I can't find the same answer as the correction, here:

syms A;

syms k;

syms q(I);

syms q(E);

syms beta;

q(I)=A/3+beta*k/3;

q(E)=A/3+beta*k/3;

k=2*A*beta/(9-2*beta^2);

f=A*q(I)+beta*k*q(I)-q(I)^2-q(E)*q(I)-k^2/2;

solve(f)

if beta= [0,1], beta~=3/sqrt (2) ~= -3/sqrt (2)

According to the calculation on Matlab I find

f= -(A*(8*beta^2 - 9))/(2*beta*(2*beta^2 - 9)) and according to the correction f=A^2/(9-2*beta^2)

I don't know where the error came from.

Thank you in advance for your answers