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4777222
@4777222
May 2022
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(х^2-5х+7)(х-2)(х-3)=2
Решите уравнение, тут нужна замена
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KuOV
Verified answer
(x² - 5x + 7)(x² - 5x + 6) = 2
x² - 5x + 6 = t
(t + 1)·t = 2
t² + t - 2 = 0
D = 1 + 8 = 9
t = (- 1 - 3)/2 = - 2 t = (- 1 + 3)/2 = 1
x² - 5x + 6 = - 2 x² - 5x + 6 = 1
x² - 5x + 8 = 0 x² - 5x + 5 = 0
D = 25 - 32 < 0 D = 25 - 20 = 5
нет корней x = (5 - √5)/2 или x = (5 + √5)/2
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Answers & Comments
Verified answer
(x² - 5x + 7)(x² - 5x + 6) = 2x² - 5x + 6 = t
(t + 1)·t = 2
t² + t - 2 = 0
D = 1 + 8 = 9
t = (- 1 - 3)/2 = - 2 t = (- 1 + 3)/2 = 1
x² - 5x + 6 = - 2 x² - 5x + 6 = 1
x² - 5x + 8 = 0 x² - 5x + 5 = 0
D = 25 - 32 < 0 D = 25 - 20 = 5
нет корней x = (5 - √5)/2 или x = (5 + √5)/2