12. Найдите значение выражения х(х-16) – (х+8)(х – 8) при х = 19 8

Ответ: -36.5

Подставим значение \(x = \frac{19}{8}\) в выражение \(x(x-16) - (x+8)(x-8)\):

\[\frac{19}{8}\left(\frac{19}{8}-16\right) - \left(\frac{19}{8}+8\right)\left(\frac{19}{8}-8\right) = \frac{19}{8}\left(\frac{19}{8}-\frac{128}{8}\right) - \left(\frac{19}{8}+\frac{64}{8}\right)\left(\frac{19}{8}-\frac{64}{8}\right)\]

\[= \frac{19}{8}\left(-\frac{109}{8}\right) - \left(\frac{83}{8}\right)\left(-\frac{45}{8}\right) = -\frac{2071}{64} + \frac{3735}{64} = \frac{1664}{64} = \frac{26}{1} = 26 \]

\[ = \frac{19}{8}(\frac{19}{8} - 16) - (\frac{19}{8} + 8)(\frac{19}{8} - 8) = \frac{19}{8}(\frac{19-128}{8}) - (\frac{19+64}{8})(\frac{19-64}{8}) = \frac{19}{8}(\frac{-109}{8}) - (\frac{83}{8})(\frac{-45}{8}) = \frac{-2071}{64} + \frac{3735}{64} = \frac{1664}{64} = 26\]

\[ x(x - 16) - (x + 8)(x - 8) = x^2 - 16x - (x^2 - 64) = x^2 - 16x - x^2 + 64 = -16x + 64 \]

\[ -16 \cdot \frac{19}{8} + 64 = -2 \cdot 19 + 64 = -38 + 64 = 26 \]

\[ x = \frac{19}{8} = 2.375 \]

\[ -16 \cdot 2.375 + 64 = -38 + 64 = 26 \]

Упростим выражение:

\[ x(x - 16) - (x + 8)(x - 8) = x^2 - 16x - (x^2 - 64) = x^2 - 16x - x^2 + 64 = -16x + 64 \]

Подставим \(x = \frac{19}{8}\):

\[ -16 \cdot \frac{19}{8} + 64 = -2 \cdot 19 + 64 = -38 + 64 = 26 \]

Ответ: 26