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yby24
@yby24
August 2022
2
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Решить уравнение с подробным объяснением.
(x^2 + 1/x^2) + (x + 1/x)=0
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katli2
Вот решение ...........
2 votes
Thanks 0
yby24
Благодарю!
pavlikleon
а почему х=0.5+i*(3)^0.5 не решение?
pavlikleon
х^3+1=0 имеет три решения
pavlikleon
х=0,5(1+i*(3)^(0.5))
aeaes1215
T = x + 1/x
t^2 = x^2 + 1/x^2 + 2
t^2 + t - 2 = 0
D = 1 + 8 = 3^2
t1 = (-1 - 3)/ 2 = -2 => x + 1/x + 2 = 0 => x^2 + 2x + 1 = 0
(x + 1)^2 = 0
x = -1
t2 = (-1 + 3)/2 = 1 => x + 1/x - 1 = 0 => x^2 -x + 1 = 0
D = 1 - 4 < 0; нет корней
Ответ x = -1
1 votes
Thanks 0
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Answers & Comments
t^2 = x^2 + 1/x^2 + 2
t^2 + t - 2 = 0
D = 1 + 8 = 3^2
t1 = (-1 - 3)/ 2 = -2 => x + 1/x + 2 = 0 => x^2 + 2x + 1 = 0
(x + 1)^2 = 0
x = -1
t2 = (-1 + 3)/2 = 1 => x + 1/x - 1 = 0 => x^2 -x + 1 = 0
D = 1 - 4 < 0; нет корней
Ответ x = -1