Question

Найди корни уравнения (5x−14)2−5(5x−14)+6=0

Answer 1

${(5x - 14)}^{2} - 5(5x - 14) + 6 = 0 \\ 5x - 14 = t \\ {t}^{2} - 5t + 6 = 0 \\ d = {b}^{2} - 4ac = 25 - 4 \times 6 = 25 - 24 = 1 \\ t1 = \frac{5 + 1}{2} = \frac{6}{2} = 3 \\ t2 = \frac{5 - 1}{2} = \frac{4}{2} = 2 \\ 1) \: 5x - 14 = 3 \\ 5x = 17 \\ x = \frac{17}{5} = 3.4 \\ 2) \: 5x - 14 = 2 \\ 5x = 16 \\ x = \frac{16}{5} = 3.2$
Ответ: 3.2; 3.4