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sonyar2507
@sonyar2507
October 2021
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решите пожалуйста уравнение^^
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ShirokovP
Verified answer
(x^4 + x^2)^2 - x^4 - x^2 = 2
Пусть x^2 = t
(t^2 + t)^2 - t^2 - t = 2
(t^2 + t)^2 - 1* (t^2 + t) - 2 = 0
(t^2 + t - 2 )* (t^2 + t + 1) = 0
1) t^2 + t - 2 = 0
(t + 2) ( t - 1)= 0
t1 = - 2; ==> не удовлетворяет ОДЗ
t2 = 1 ==> удовлетворяет ОДЗ
2) t^2 + t + 1 = 0
D = 1 - 4 < 0
Возвращаемся обратно к замене:
x^2 = 1
x1 = - 1
x2 = 1
ОТВЕТ:
- 1; 1
2 votes
Thanks 1
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Answers & Comments
Verified answer
(x^4 + x^2)^2 - x^4 - x^2 = 2Пусть x^2 = t
(t^2 + t)^2 - t^2 - t = 2
(t^2 + t)^2 - 1* (t^2 + t) - 2 = 0
(t^2 + t - 2 )* (t^2 + t + 1) = 0
1) t^2 + t - 2 = 0
(t + 2) ( t - 1)= 0
t1 = - 2; ==> не удовлетворяет ОДЗ
t2 = 1 ==> удовлетворяет ОДЗ
2) t^2 + t + 1 = 0
D = 1 - 4 < 0
Возвращаемся обратно к замене:
x^2 = 1
x1 = - 1
x2 = 1
ОТВЕТ:
- 1; 1