# Not AM-GM

Algebra Level 4

Find the maximum value of $\ \frac { a }{ c } + \frac { b }{ d } + \frac { c }{ a } + \frac { d }{ b },$ where $a,b,c,d$ vary over all distinct real numbers such that $\frac { a }{ b } + \frac { b }{ c } + \frac { c }{ d } + \frac { d }{ a } = 4$ and $ac = bd$.

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