Symmetric Matrices & Quadratic Forms · Hard problem

Two quadratic forms have matrices $A_1=\begin{pmatrix}1&0\\0&4\end{pmatrix}$ (eigenvalues $1,4$) and $A_2=\begin{pmatrix}2&-1\\-1&2\end{pmatrix}$ (eigenvalues $1,3$); both are positive definite. Their sum $A_1+A_2$ is automatically positive definite too — but its eigenvalues are NOT simply the sums $1+1$ and $4+3$ of the individual eigenvalues. Find the SMALLER eigenvalue of $A_1+A_2$.