Random Matrices and a Random Equation

Level pending

\(Let\quad the\quad solutions\quad to\quad this\quad equation\quad be\quad \alpha \quad and\quad \beta .\\ f\left( x \right) =\sqrt { x } -3\sqrt [ 4 ]{ x } -10\\ \\ More\quad precisely,\quad \alpha >\beta \\ \\ \begin{pmatrix} \psi & 2 \\ 5 & 1 \end{pmatrix}\begin{pmatrix} 6 & 2 \\ 5 & 4 \end{pmatrix}=\begin{pmatrix} \beta & \sqrt { \alpha } -15 \\ 35 & 14 \end{pmatrix}\\ \\ Find\quad { \alpha }^{ 2 }+{ \beta }^{ 2 }+\psi\)

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