Question

решите систему!! x²+12xy+36y²=121 x-3y=8

Answer 1

$\displaystyle\bf\\\left \{ {{ {x}^{2} + 12xy + 36 {y}^{2} = 121} \atop {x - 3y = 8 }} \right. \\ \displaystyle\bf\\\left \{ {{(3y + 8) {}^{2} + 12y(3y + 8) + 36 {y}^{2} = 121 } \atop {x = 3y + 8}} \right. \\ \\(3y + 8) {}^{2} + 12y(3y + 8) + 36 {y}^{2} = 121 \\ (3y + 8 + 6y) {}^{2} = 121 \\ (9y + 8) {}^{2} - 11 {}^{2} = 0 \\ (9y + 8 - 11)(9y + 8 + 11) = 0 \\(9y - 3)(9y + 19) = 0 \\ 1) \: 9y - 3 = 0 \\ 9y = 3 \\ y = \frac{3}{9} \\ y _{1}= \frac{1}{3} \\ 2) \: 9y + 19 = 0 \\ 9y = - 19 \\ y = - \frac{19}{9} \\ y_{2} = - 2 \frac{1}{9 } \\ \\ x_{1} = 3 \times \frac{1}{3} + 8 = 1 + 8 = 9 \\ x_{2} = 3 \times( - \frac{19}{9}) + 8 = - \frac{19}{3} + 8 = - 6 \frac{1}{3} + 8 = 1 \frac{2}{3}$

Ответ: ( 9 ; 1/3 ) и ( 1 2/3 ; - 2 1/9 )