Question

Укажите промежуток, содержащий корни уравнения
Помогите, пожалуйста!

Answer 1

$log_{sin bigg {frac{pi}{4}} } (x^{2} - 5x + 8) = -4$

$log_bigg{frac{sqrt{2}}{2} } (x^{2} - 5x + 8) = -4$

$log_bigg{frac{sqrt{2}}{2} } (x^{2} - 5x + 8) = log_bigg{frac{sqrt{2}}{2} } left( dfrac{sqrt{2}}{2} right)^{-4}$

$log_bigg{frac{sqrt{2}}{2} } (x^{2} - 5x + 8) = log_bigg{frac{sqrt{2}}{2} } left( dfrac{2}{sqrt{2}} right)^{4}$

$log_bigg{frac{sqrt{2}}{2} } (x^{2} - 5x + 8) = log_bigg{frac{sqrt{2}}{2} } left( sqrt{2} right)^{4}$

$log_bigg{frac{sqrt{2}}{2} } (x^{2} - 5x + 8) = log_bigg{frac{sqrt{2}}{2} } 4$

$x^{2} - 5x + 8 = 4$

$x^{2} - 5x + 4 = 0$

$left{begin{array}{ccc}x_{1} + x_{2} = 5,\x_{1}x_{2} = 4 \end{array}right$

$x_{1} = 4\x_{2} = 1$

Ответ: В) (0; 5).