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

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

Answered by ajfour last updated on 05/Feb/18

$$3x-\frac{8}{x}=12$$$$3x^2-12x=8$$$$3(x^2-4x)=8$$$$3{(x-2)}^2=20$$$$x=2\pm 2\sqrt{\frac{5}{3}}$$$$y=\frac{1}{1\pm \sqrt{\frac{5}{3}}}=\frac{1\mp \sqrt{\frac{5}{3}}}{-\frac{2}{3}}$$$$(x_1,y_1)\equiv [2(1+\sqrt{\frac{5}{3}}),\frac{3}{2}(\sqrt{\frac{5}{3}}-1)]$$$$(x_2,y_2)\equiv [2(1-\sqrt{\frac{5}{3}}),-\frac{3}{2}(\sqrt{\frac{5}{3}}+1)].$$

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