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omigovich
@omigovich
July 2022
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решите уравнения (x^2+x-5)(x^2+x+1)=-9
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ShirokovP
Verified answer
Пусть t = x^2 + x, тогда
(t - 5)(t + 1) = - 9
(t - 5)(t + 1) + 9 = 0
t^2 + t - 5t - 5 + 9 = 0
t^2 - 4t + 4 = 0
D = 16 - 16 = 0
t = - b/2a = 4/2= 2
Возвращаемся обратно
x^2 + x = 2
x^2 + x - 2 = 0
D = 9
x1 = ( - 1 - 3)/2 = - 2
x2 = ( - 1 + 3)/2 = 1
Ответ
- 2 ; 1
5 votes
Thanks 14
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Answers & Comments
Verified answer
Пусть t = x^2 + x, тогда(t - 5)(t + 1) = - 9
(t - 5)(t + 1) + 9 = 0
t^2 + t - 5t - 5 + 9 = 0
t^2 - 4t + 4 = 0
D = 16 - 16 = 0
t = - b/2a = 4/2= 2
Возвращаемся обратно
x^2 + x = 2
x^2 + x - 2 = 0
D = 9
x1 = ( - 1 - 3)/2 = - 2
x2 = ( - 1 + 3)/2 = 1
Ответ
- 2 ; 1