Question

Решить систему уравнении полностью {3x^2+2y^2=45 {9x^2+6x^2=45

Answer 1

Объяснение:

$\left \{ \begin{array}{lcl}3 {x}^{2} + 2 {y}^{2} = 45 \: \: \: \: \: \: \times ( - 3)\\9 {x}^{2} + 6 {y}^{2} = 45x \end{array} \right. \\ \left \{ \begin{array}{lcl} - 9 {x}^{2} - 6 {y}^{2} = - 135\\9 {x}^{2} + 6 {y}^{2} = 45x\end{array} \right. \\ \left \{ \begin{array}{lcl}0 = 45x - 135 \\3 {x}^{2} + 2 {y}^{2} = 45\end{array} \right. \\ \left \{ \begin{array}{lcl}x = 3\\3 \times {3}^{2} + 2 {y}^{2} = 45 \end{array} \right. \\ \left \{ \begin{array}{lcl} {y}^{2} = 9 \\x = 3 \end{array} \right. \\ \left [ \begin{array}{lcl}\left \{ \begin{array}{lcl} y = 3 \\ x =3 \end{array} \right.\ \\ \left \{ \begin{array}{lcl} y = -3 \\ x =3 \end{array} \right. \end{array} \right.$

(3; 3) и (3; -3)

ответ: (3; 3), (3; -3)