Twin Quadratic Constraints

Problem

The system

\begin{cases} x^2 - 3xy = 2016, \\ y^2 - 3xy = 2017 \end{cases}

has two solutions $(x_1, y_1)$ and $(x_2, y_2)$ with $\dfrac{x_1}{y_1} \ne \dfrac{x_2}{y_2}$ . Find

\frac{(y_1 - x_1)(y_2 - x_2)}{y_1 y_2}.

Answer

Solution

Difficulty	5/10
Topics	algebra, Vieta's Formulas

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