\[\boxed{\text{301\ (301).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]
\[\textbf{а)}\ \frac{12 - 5x - 2x^{2}}{15 - 10x}\]
\[- 2x^{2} - 5x + 12 = 0\]
\[2x^{2} + 5x - 12 = 0\]
\[D = 25 + 4 \cdot 2 \cdot 12 = 25 + 9121\]
\[x_{1,2} = \frac{- 5 \pm 11}{4} = - 4;\frac{3}{2};\]
\[12 - 5x - 2x^{2} =\]
\[= - 2 \cdot (x + 4)\left( x - \frac{3}{2} \right) =\]
\[= (x + 4)(3 - 2x);\]
\[\Longrightarrow \frac{12 - 5x - 2x^{2}}{15 - 10x} =\]
\[= \frac{(x + 4)(3 - 2x)}{5 \cdot (3 - 2x)} = \frac{x + 4}{5}.\]
\[\textbf{б)}\ \frac{3x^{2} - 36x - 192}{x^{2} - 256}\]
\[3x^{2} - 36x - 192 = 0\ \ \ \ \ |\ :3\ \]
\[x^{2} - 12x - 64 = 0\]
\[D_{1} = 6^{2} + 64 = 100\]
\[x_{1,2} = 6 \pm 10 = 16;\ - 4;\]
\[3x^{2} - 36x - 192 =\]
\[= 3 \cdot (x - 16)(x + 4);\]
\[\ \Longrightarrow \frac{3x^{2} - 36x - 192}{x^{2} - 256} =\]
\[= \frac{3 \cdot (x - 16)(x + 4)}{(x - 16)(x + 16)} =\]
\[= \frac{3 \cdot (x + 4)}{x + 16} = \frac{3x + 12}{x + 16}.\]
\[\boxed{\text{301.}\text{\ }\text{ОК\ ГДЗ\ -\ домашка\ на\ 5}}\]
\[x^{4} - x^{3} - 51x^{2} + 49x + 98 = 0\]
\[Схема\ Горнера:\]
\[1\] | \[- 1\] | \[- 51\] | \[49\] | \[98\] | |
---|---|---|---|---|---|
\[- 1\] | \[1\] | \[- 2\] | \[- 49\] | \[98\] | |
\[2\] | \[1\] | \[0\] | \[- 49\] | \[0\] | |
\[7\] | \[1\] | \[7\] | \[0\] | ||
\[- 7\] | \[1\] | \[0\] |
\[x = - 7;\ - 1;2;7.\]