Bounds on the autocorrelations of an AR(2) process I need to prove

I want to get some hints on it, I know the condition of stationary, and what the model should look like, but I dont 't know how to show it. I have tried to take the difference between the two and try to show that this is smaller then zero. But I am unable to find something to bound it.
 A: OK, next hint - too lengthy for a comment:
We have \begin{eqnarray*}
  0\leq  Var(\alpha_0Y_t+\alpha_1Y_{t-1}+\alpha_2Y_{t-2})&=&Var\left(\begin{pmatrix}
    \alpha_0&\alpha_1&\alpha_2
    \end{pmatrix}\begin{pmatrix}
    Y_t\\Y_{t-1}\\Y_{t-2}
    \end{pmatrix}\right)\\
    &=&\begin{pmatrix}
    \alpha_0&\alpha_1&\alpha_2
    \end{pmatrix}Var\begin{pmatrix}
    Y_t\\Y_{t-1}\\Y_{t-2}
    \end{pmatrix}\begin{pmatrix}
    \alpha_0\\\alpha_1\\\alpha_2
    \end{pmatrix}\\
    &=&\begin{pmatrix}
    \alpha_0&\alpha_1&\alpha_2
    \end{pmatrix} \begin{pmatrix}
    \gamma_0&\gamma_1&\gamma_2\\
    \gamma_1&\gamma_0&\gamma_1\\
    \gamma_2&\gamma_1&\gamma_0
    \end{pmatrix}\begin{pmatrix}
    \alpha_0\\\alpha_1\\\alpha_2
    \end{pmatrix}\\
    &=&\gamma_0\begin{pmatrix}
    \alpha_0&\alpha_1&\alpha_2
    \end{pmatrix} \begin{pmatrix}
    1&\rho_1&\rho_2\\
    \rho_1&1&\rho_1\\
    \rho_2&\rho_1&1
    \end{pmatrix}\begin{pmatrix}
    \alpha_0\\\alpha_1\\\alpha_2
    \end{pmatrix}
    \end{eqnarray*}
Here, the $\alpha_j$ are arbitrary constants, the $\gamma_j$ are (autoco)variances and the $\rho_j$ autocorrelations.
Now, use conditions for positive semi-definiteness of a matrix.
