Найдите значение дроби: (y^2-11y-26)/(9y+18) при y=-5; 31; 112.

Ответ:

\[\frac{y^{2} - 11y - 26}{9y + 18} =\]

\[= \frac{(y - 13)(y + 2)}{9(y + 2)} = \frac{y - 13}{9}\ \]

\[y^{2} - 11y - 26 = 0\]

\[y_{1} + y_{2} = 11;\ \ \ \ y_{1} \cdot y_{2} = - 26\]

\[y_{1} = 13;\ \ \ y_{2} = - 2.\]

\[y = - 5:\]

\[\frac{y - 13}{9} = \frac{- 5 - 13}{9} = - \frac{18}{9} = - 2.\]

\[y = 31:\]

\[\frac{y - 13}{9} = \frac{31 - 13}{9} = \frac{18}{9} = 2.\]

\[y = 112:\]

\[\frac{y - 13}{9} = \frac{112 - 13}{9} = \frac{99}{9} = 11.\]