Question

помогите пожалуйста дам 100 балов ​

Answer 1

а)

$\displaystyle\bf\\\left \{ {{y = 3x - 2} \atop {y = {x}^{2} }} \right. \\ \\ {x}^{2} = 3x - 2 \\ {x}^{2} - 3x + 2 = 0 \\ a = 1 \\ b = - 3\\ c = 2\\ D = {b}^{2} - 4ac = ( - 3) {}^{2} - 4 \times 1 \times 2 = 9 - 8 = 1 \\ x_{1} = \frac{3 - 1}{2} = \frac{2}{2} = 1 \\ x_{2} = \frac{3 + 1}{2} = \frac{4}{2} = 2 \\ \\ y_{1} = 1 {}^{2} = 1 \\ y_{2} = {2}^{2} = 4$

Ответ: ( 1 ; 1 ) и ( 2 ; 4 )

б)

$\displaystyle\bf\\\left \{ {{x = 2y + 1} \atop {xy + y = 4 }} \right. \\ \\ y(2y + 1) + y = 4 \\ 2 {y}^{2} + y + y - 4 = 0 \\ 2 {y}^{2} + 2y - 4 = 0 \\ {y}^{2} + y - 2 = 0 \\ a =1 \\ b =1 \\ c = - 2\\ D = {b}^{2} - 4ac = {1}^{2} - 4 \times 1 \times ( - 2) = 1 + 8 = 9 \\ y_{1} = \frac{ - 1 - 3}{2} = - \frac{4}{2} = - 2 \\ y_{2} = \frac{ - 1 + 3}{2} = \frac{2}{2} = 1 \\ \\ x_{1} = 2 \times ( - 2) + 1 = - 4 + 1 = - 3 \\ x_{2} = 2 \times 1 + 1 = 2 + 1 = 3$

Ответ: ( - 3 ; - 2 ) и ( 3 ; 1 )

в)

$\displaystyle\bf\\\left \{ {{3 {x}^{2} + {y}^{2} = 7} \atop {y = 2x }} \right. \\ \\ 3 {x}^{2} + (2x) {}^{2} = 7 \\ 3 {x}^{2} + 4 {x}^{2} = 7 \\ 7 {x}^{2} = 7 \\ {x}^{2} = 1 \\ x_{1} = - 1 \\ x_{2} = 1 \\ \\ y_{1} = 2 \times ( - 1) = - 2 \\ y_{2} = 2 \times 1 = 2$

Ответ: ( - 1 ; - 2 ) и ( 1 ; 2 )