Question

Решите примеры с очень детальным разъяснениям

Answer 1

$1)\frac{x}{y} = t \\ t + \frac{1}{t} = \frac{26}{5} \\ \frac{ {t}^{2} + 1 }{t} = \frac{26}{5} \\ 5 {t}^{2} +5 = 26 t \\ 5 {t}^{2} - 26t + 5 = 0 \\ dis = 676 - 100 = 576 \\ t1 = \frac{26 + 24}{10} = 5 \\ t2 = \frac{26 - 24}{10} = \frac{1}{5} \\ a)\frac{x}{y} = 5 \: \: \: \: x = 5y \\ ( {5y})^{2} - {y}^{2} = 96 \\ 24 {y}^{2} = 96 \\ {y}^{2} = 4 \\ y1 = 2 \: \: \ \: \: \: \: \: \: \: \: \: \: \: x1 = 5 \times 2 = 10\\ y2 = - 2 \: \: \: \: \: \: \: \: \: \: x2 = 5 \times - 2 = - 10 \\ b) \frac{x}{y} = \frac{1}{5} \\ y = 5x \\ {x}^{2} = 25 {x}^{2} = 96 \\ = 24 {x}^{2} = 96 \\ {x}^{2} = - 4 \: net \: korney \\ znacit \: t = \frac{1}{5} \: ne \: udovletvoraet \: usloviyu$

$\frac{x}{y} = t \\ t - \frac{2}{t} = \frac{7}{3} \\ \frac{ {t}^{2} - 2}{t} = \frac{7}{ 3} \\ 3 {t}^{2} - 6 = 7t \\ 3 {t}^{2} - 7t - 6 = 0 \\ dis = 121 \\ t1 = \frac{7 + 11}{6} = 3 \\ t2 = \frac{7 - 11}{6} = - \frac{2}{3} \\ a) \frac{x}{y} = 3 \\ x = 3y \\ {(3y)}^{2} + {y}^{2} = 40 \\ 10 {y}^{2} = 40 \\ {y}^{2} = 4 \\ y1 = 2 \: \: \: \: \: \: \: x1 = 3 \times 2 = 6 \\ y2 = - 2 \: \: \: \: \: \: x2 = 3 \times ( - 2) = - 6 \\ b) \frac{x}{y} = - \frac{2}{3} \\ x = - \frac{2}{3} y \\ {{( - \frac{2}{3}y }) }^{2} + y^{2} = 40 \\ \frac{4}{9} {y}^{2} + {y}^{2} = 40 \\ \frac{13}{9} {y}^{2} = 40 \\ {y}^{2} = \frac{360}{13} \\ y1 = \frac{6 \sqrt{10} }{ \sqrt{13} } = \frac{6 \sqrt{130} }{13} \\ x1 = - \frac{2}{3} \times \frac{6 \sqrt{130} }{13} = - \frac{4 \sqrt{130} }{13} \\ y2 = - \frac{ 6 \sqrt{130} }{13} \: \: \: \: \: \: \\ x2 = \frac{4 \sqrt{130} }{13}$