Question

решите уравнение (ײ-5×+9)(ײ-5×+13)=45

Answer 1

Ответ:

$( {x}^{2} - 5x + 9)( {x}^{2} - 5x + 13) = 45 \\ ( {x}^{2} - 5x + 9)( {x}^{2} - 5x + 9 + 4) = 45$

Замена:

$x {}^{2} - 5x + 9 = t \\ \\ t(t + 4)= 45 \\ {t}^{2} + 4t - 45 = 0 \\ D = 16 + 180 = 196\\ t_1 = \frac{ - 4 + 14}{2} = 5 \\ t_2 = - 9 \\ \\ {x}^{2} - 5x + 9 = 5 \\ {x}^{2} - 5x + 4 = 0 \\ D = 25 - 16 = 9 \\ x_1 = \frac{5 + 3 }{2}=4 \\ x_2 = \frac{5 - 3 }{2} =1\\ \\ {x}^{2} - 5x + 9 = - 9 \\ {x}^{2} - 5x + 18 = 0 \\ D = 25 - 4 \times 18 < 0$

нет корней

Ответ: 1; 4