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alina991129
@alina991129
July 2022
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(x^2+x^2)^2-8(x^2+x)+12=0 решите уравнение
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ShirokovP
Verified answer
Пусть x^2 + x = t, тогда
t^2 - 8t + 12 = 0
D = 64 - 48 = 16
t1 = (8 + 4)/2 = 12/2 = 6
t2 = (8 - 4)/2 = 4/2 = 2
Обратная замена
1) x^2 + x = 6
x^2 + x - 6 = 0
D = 1 + 24 = 25
x1 = ( - 1 + 5)/2 = 4/2 = 2
x2 = ( - 1 - 5)/2 = - 6/2 = - 3
2) x^2 + x = 2
x^2 + x - 2 = 0
D = 1 + 8 = 9
x3 = ( - 1 + 3)/2 = 2/2 = 1
x4 = ( - 1 - 3)/2 = - 4/2 = - 2
Ответ
- 3; - 2; 1; 2
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Answers & Comments
Verified answer
Пусть x^2 + x = t, тогдаt^2 - 8t + 12 = 0
D = 64 - 48 = 16
t1 = (8 + 4)/2 = 12/2 = 6
t2 = (8 - 4)/2 = 4/2 = 2
Обратная замена
1) x^2 + x = 6
x^2 + x - 6 = 0
D = 1 + 24 = 25
x1 = ( - 1 + 5)/2 = 4/2 = 2
x2 = ( - 1 - 5)/2 = - 6/2 = - 3
2) x^2 + x = 2
x^2 + x - 2 = 0
D = 1 + 8 = 9
x3 = ( - 1 + 3)/2 = 2/2 = 1
x4 = ( - 1 - 3)/2 = - 4/2 = - 2
Ответ
- 3; - 2; 1; 2