Question

Розв'яжіть систему рівнянь​

Answer 1

$\displaystyle\bf\\\left \{ {{x - 2y = 5} \atop { {x}^{2} - 2xy - 3 {y}^{2} = - 7 }} \right. \\ \displaystyle\bf\\\left \{ {{x = 2y + 5} \atop {(2y + 5) {}^{2} - 2y(2y + 5) - 3 {y}^{2} = - 7 }} \right. \\ \\ 4 {y}^{2} + 20y + 25 - 4 {y}^{2} - 10y - 3 {y}^{2} + 7 = 0 \\ - 3 {y}^{2} + 10y + 32 = 0 \\ 3 {y}^{2} - 10y - 32 = 0 \\ a =3 \\ b = - 10\\ c = - 32 \\ D = {b}^{2} - 4ac = ( - 10) {}^{2} - 4 \times 3 \times ( - 32) = \\ = 100 + 384 = 484 \: \: ( \sqrt{D} = 22) \\ y_{1} = \frac{10 - 22}{2 \times 3} = - \frac{12}{6} = - 2 \\ y_{2} = \frac{10 + 22}{2 \times 3} = \frac{32}{6} = \frac{16}{3} = 5 \frac{1}{3} \\ \\ x_{1} = 2 \times ( - 2) + 5 = - 4 + 5 = 1 \\ x_{2} = 2 \times 5 \frac{1}{3} + 5 = 10 \frac{2}{3} + 5 = 15 \frac{2}{3}$

Ответ: ( 1 ; - 2 ) и ( 15 2/3 ; 5 1/3 )