Delta-rational chord: Difference between revisions

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The unique solution with x > 0 is

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\displaystyle { \left( \frac{2 \delta_{1} + \delta_{3} + \frac{2 \left(- 2 \delta_{1}^{2} f_{1} + \delta_{1}^{2} f_{2} + \delta_{1}^{2} f_{3} - \delta_{1} \delta_{3} f_{1} + \delta_{1} \delta_{3} f_{2} - \delta_{1} \delta_{3} f_{3} + \delta_{1} \delta_{3} + \delta_{3}^{2} f_{2} - \delta_{3}^{2}\right)}{2 \delta_{1} f_{1} - 2 \delta_{1} - \delta_{3} f_{2} + \delta_{3} f_{3}}}{f_{2} + f_{3} - 2}, \ \frac{- 2 \delta_{1}^{2} f_{1} + \delta_{1}^{2} f_{2} + \delta_{1}^{2} f_{3} - \delta_{1} \delta_{3} f_{1} + \delta_{1} \delta_{3} f_{2} - \delta_{1} \delta_{3} f_{3} + \delta_{1} \delta_{3} + \delta_{3}^{2} f_{2} - \delta_{3}^{2}}{2 \delta_{1} f_{1} - 2 \delta_{1} - \delta_{3} f_{2} + \delta_{3} f_{3}}\right).}

(x, y) = \displaystyle { \left( \frac{2 \delta_{1} + \delta_{3} + \frac{2 \left(- 2 \delta_{1}^{2} f_{1} + \delta_{1}^{2} f_{2} + \delta_{1}^{2} f_{3} - \delta_{1} \delta_{3} f_{1} + \delta_{1} \delta_{3} f_{2} - \delta_{1} \delta_{3} f_{3} + \delta_{1} \delta_{3} + \delta_{3}^{2} f_{2} - \delta_{3}^{2}\right)}{2 \delta_{1} f_{1} - 2 \delta_{1} - \delta_{3} f_{2} + \delta_{3} f_{3}}}{f_{2} + f_{3} - 2}, \ \frac{- 2 \delta_{1}^{2} f_{1} + \delta_{1}^{2} f_{2} + \delta_{1}^{2} f_{3} - \delta_{1} \delta_{3} f_{1} + \delta_{1} \delta_{3} f_{2} - \delta_{1} \delta_{3} f_{3} + \delta_{1} \delta_{3} + \delta_{3}^{2} f_{2} - \delta_{3}^{2}}{2 \delta_{1} f_{1} - 2 \delta_{1} - \delta_{3} f_{2} + \delta_{3} f_{3}}\right).}

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 The unique solution with x > 0 is
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-\displaystyle { \left( \frac{2 \delta_{1} + \delta_{3} + \frac{2 \left(- 2 \delta_{1}^{2} f_{1} + \delta_{1}^{2} f_{2} + \delta_{1}^{2} f_{3} - \delta_{1} \delta_{3} f_{1} + \delta_{1} \delta_{3} f_{2} - \delta_{1} \delta_{3} f_{3} + \delta_{1} \delta_{3} + \delta_{3}^{2} f_{2} - \delta_{3}^{2}\right)}{2 \delta_{1} f_{1} - 2 \delta_{1} - \delta_{3} f_{2} + \delta_{3} f_{3}}}{f_{2} + f_{3} - 2}, \  \frac{- 2 \delta_{1}^{2} f_{1} + \delta_{1}^{2} f_{2} + \delta_{1}^{2} f_{3} - \delta_{1} \delta_{3} f_{1} + \delta_{1} \delta_{3} f_{2} - \delta_{1} \delta_{3} f_{3} + \delta_{1} \delta_{3} + \delta_{3}^{2} f_{2} - \delta_{3}^{2}}{2 \delta_{1} f_{1} - 2 \delta_{1} - \delta_{3} f_{2} + \delta_{3} f_{3}}\right).}
+(x, y) = \displaystyle { \left( \frac{2 \delta_{1} + \delta_{3} + \frac{2 \left(- 2 \delta_{1}^{2} f_{1} + \delta_{1}^{2} f_{2} + \delta_{1}^{2} f_{3} - \delta_{1} \delta_{3} f_{1} + \delta_{1} \delta_{3} f_{2} - \delta_{1} \delta_{3} f_{3} + \delta_{1} \delta_{3} + \delta_{3}^{2} f_{2} - \delta_{3}^{2}\right)}{2 \delta_{1} f_{1} - 2 \delta_{1} - \delta_{3} f_{2} + \delta_{3} f_{3}}}{f_{2} + f_{3} - 2}, \  \frac{- 2 \delta_{1}^{2} f_{1} + \delta_{1}^{2} f_{2} + \delta_{1}^{2} f_{3} - \delta_{1} \delta_{3} f_{1} + \delta_{1} \delta_{3} f_{2} - \delta_{1} \delta_{3} f_{3} + \delta_{1} \delta_{3} + \delta_{3}^{2} f_{2} - \delta_{3}^{2}}{2 \delta_{1} f_{1} - 2 \delta_{1} - \delta_{3} f_{2} + \delta_{3} f_{3}}\right).}
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