\[\boxed{\mathbf{946.ОК\ ГДЗ - домашка\ на}\ 5}\]
\[\mathbf{Дано:}\]
\[\textbf{а)}\ AB = 2;A(2;3);\]
\[B(x;1).\]
\[\textbf{б)}\ M_{1}M_{2} = 7;\]
\[M_{1}( - 1;x);M_{2}(2x;3).\]
\[\mathbf{Найти:}\]
\[x - ?\]
\[\mathbf{Решение.}\]
\[\textbf{а)}\ AB = \sqrt{(x - 2)^{2} + (1 - 3)^{2}} =\]
\[= 2:\]
\[\sqrt{(x - 2)^{2} + 4} = 2\ \]
\[(x - 2)^{2} + 4 = 4\]
\[(x - 2)^{2} = 0\]
\[x = 2.\]
\[\textbf{б)}\ M_{1}M_{2} =\]
\[= \sqrt{(2x + 1)^{2} + (3 - x)^{2}} = 7\]
\[(2x + 1)^{2} + (3 - x)^{2} = 49\]
\[4x^{2} + 4x + 1 + 9 - 6x + x^{2} = 49\]
\[5x^{2} - 2x - 39 = 0\]
\[D = b^{2} - 4ac =\]
\[= ( - 2)^{2} - 4 \bullet 5 \bullet ( - 39) =\]
\[= 4 + 7801 = 784\]
\[= 4 + 780 = 784\]
\[x_{1} = \frac{2 + 28}{10} = \frac{30}{3} = 3;\ \]
\[x_{2} = \frac{2 - 28}{10} = - \frac{26}{10} = - 2,6.\]
\[\mathbf{Ответ:}\mathbf{\ }а)\ 2;\ \ \ б)\ 3;\ - 2,6.\]