Question

Решите х^2+7х-8)(2х^2+7х-3)-6=0

Answer 1

Сделаем замену  2x² + 7x - 8 = m , тогда 2x² + 7x - 3 = m + 5
m (m + 5) - 6 = 0
m² + 5m - 6 = 0
D = 25 - 4 * 1 * (- 6) = 25 + 24 = 49 = 7²
$m _{1} = \frac{-5+7}{2}=1\\\\m _{2} = \frac{-5-7}{2}=-6$
2x² + 7x - 8 = 1                                     2x² + 7x - 8 = - 6
2x² + 7x - 9 = 0                                     2x² + 7x - 2 = 0
D = 49 - 4 * 2 * (- 9) = 121 = 11²           D = 49 - 4 * 2 * (- 2) = 65
$X _{1} = \frac{-7+11}{4}=1\\\\X _{2}= \frac{-7-11}{4}=- 4,5\\\\X _{3}= \frac{-7+ \sqrt{65} }{4}\\\\X _{4} = \frac{-7- \sqrt{65} }{4}$