14. Найдите значение выражения х(х-16)(х+8)(х-8) при х=\frac{19}{8}

Выражение: x(x-16) + (x+8)(x-8)

При x=\(\frac{19}{8}\)

x(x - 16) + (x + 8)(x - 8) = x(x - 16) + (x² - 64) = x² - 16x + x² - 64 = 2x² - 16x - 64

Подставим x = \(\frac{19}{8}\)

2(\((\frac{19}{8}\))^2 - 16(\((\frac{19}{8}\)) - 64 = 2(\(\frac{361}{64}\)) - 2 * 19 - 64 = \(\frac{361}{32}\) - 38 - 64 = \(\frac{361}{32}\) - 102 = \(\frac{361 - 32 * 102}{32}\) = \(\frac{361 - 3264}{32}\) = \(\frac{-2903}{32}\)

Выражение: x(x-16) * (x+8)(x-8)

При x=\(\frac{19}{8}\)

x(x-16)(x+8)(x-8) = x(x-16)(x²-64) = \(\frac{19}{8}\) (\(\frac{19}{8}\) - 16) ((\(\frac{19}{8}\))^2 - 64) = \(\frac{19}{8}\) (\(\frac{19 - 128}{8}\)) (\(\frac{361 - 4096}{64}\)) = \(\frac{19}{8}\) * (\(\frac{-109}{8}\)) * (\(\frac{-3735}{64}\)) = \(\frac{19 * 109 * 3735}{8 * 8 * 64}\) = \(\frac{7741965}{4096}\)

Ответ: \(\frac{7741965}{4096}\)