An algebra problem by Fidel Simanjuntak

Algebra Level 3

{x2+y2=xyx+y=12\large \begin {cases} x^2+y^2=xy \\ x+y=12\end {cases} If the above system of equations holds true for some real numbers xx and yy, find 1x+1y\dfrac{1}{x}+\dfrac{1}{y}.

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