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

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