Telling fibs

Calculus Level 5

Let the matrix with entries \(a_{ij}\) be defined as

\[\begin{pmatrix} a_{11} & a_{12} \\ a_{21} & a_{22} \end{pmatrix} = \exp \begin{pmatrix} 1 & 1 \\ 1 & 0 \end{pmatrix}\]

\[a_{12}+a_{21} = \frac{2}{\sqrt{d}}(e^{p}-e^{-1/p})\]

and \(p = \frac{a+\sqrt{b}}{c}\), where \(a,b,c,\) and \(d\) are positive integers, find \(a+b+c+d\).

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