Решите систему уравнений способом сложения: 7(x+2)^3+2(y+1)^2=1; 3(x+2)^3-2(y+1)^2=-11.

Ответ:

\[\left\{ \begin{matrix} 7(x + 2)^{3} + 2(y + 1)^{2} = 1\ \ \ \ \ \\ 3(x + 2)^{3} - 2(y + 1)^{2} = - 11 \\ \end{matrix} \right.\ ( + )\]

\[10(x + 2)^{3} = - 10\]

\[(x + 2)^{3} = - 1\]

\[x + 2 = - 1\]

\[x = - 3.\]

\[7 \cdot ( - 1) + 2\left( y^{2} + 2y + 1 \right) = 1\]

\[- 7 - 1 + 2y^{2} + 4y + 2 = 0\]

\[2y^{2} + 4y - 6 = 0\]

\[y^{2} + 2y - 3 = 0\]

\[D_{1} = 1 + 3 = 4\]

\[y_{1} = - 1 + 2 = 1;\]

\[y_{2} = - 1 - 2 = - 3.\]

\[Ответ:( - 3;1);( - 3; - 3).\]