\[\boxed{\text{1143\ (1143).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]
\[1)\ 81 \cdot 3^{2} = 3^{4} \cdot 3^{2} = 3^{6} = 729\]
\[2)\ 4^{3} \cdot 8^{2} = \left( 2^{2} \right)^{3} \cdot \left( 2^{3} \right)^{2} =\]
\[= 2^{6} \cdot 2^{6} = 2^{12} = 4096\]
\[3)\ 100^{2} \cdot 1000^{3} =\]
\[= \left( 10^{2} \right)^{2} \cdot \left( 10^{3} \right)^{3} = 10^{4} \cdot 10^{9} =\]
\[= 10^{13} = 10\ 000\ 000\ 000\ 000\ \]
\[\boxed{\text{1143.\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]
\[1)\ x² + 10y + 30 =\]
\[= 10x - y^{2} - 20\]
\[x^{2} + 10y + 30 - 10x + y^{2} + 20 =\]
\[= 0\]
\[\left( x^{2} - 10x + 25 \right) + \left( y^{2} + 10y + 25 \right) =\]
\[= 0\]
\[(x - 5)^{2} + (y + 5)^{2} = 0\]
\[x = 5,\ \ y = - 5\]
\[Ответ:(5;\ - 5).\]
\[2)\ 4x² + y² + 4x = 2y - 3\]
\[4x^{2} + y^{2} + 4x - 2y + 3 = 0\]
\[\left( 4x^{2} + 4x + 1 \right) + \left( y^{2} - 2y + 1 \right) =\]
\[= - 1\]
\[(2x + 1)^{2} + (y - 1)^{2} = - 1\]
\[Ответ:нет\ корней.\]