3x-4y-12-xy-2-

Question Number 29222 by imamu222 last updated on 05/Feb/18

3 x - 4 y = 12, x y = 2

Answered by ajfour last updated on 05/Feb/18

3 x - \frac{8}{x} = 12

3 x^{2} - 12 x = 8

3 (x^{2} - 4 x) = 8

3 {(x - 2)}^{2} = 20

x = 2 \pm 2 \sqrt{\frac{5}{3}}

y = \frac{1}{1 \pm \sqrt{\frac{5}{3}}} = \frac{1 \mp \sqrt{\frac{5}{3}}}{- \frac{2}{3}}

(x_{1}, y_{1}) \equiv [2 (1 + \sqrt{\frac{5}{3}}), \frac{3}{2} (\sqrt{\frac{5}{3}} - 1)]

(x_{2}, y_{2}) \equiv [2 (1 - \sqrt{\frac{5}{3}}), - \frac{3}{2} (\sqrt{\frac{5}{3}} + 1)] .

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