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Frogalino
@Frogalino
August 2022
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Решить уравнение:
1) x^4 + 35x^2 - 36 =0
2) x^4 - 9x^2 + 14 =0
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Answers & Comments
NightOwl1
1) x^4 + 35x^2 - 36 = 0
Замена: x^2=t
t^2 + 35t - 36 = 0
a+b+c=0 ⇒ t1 = 1; t2 = c/a = 36
x^2 = 1 и x^2 = 36
x=±1 x=
±6
Ответ: ±1,
±6
2) x^4 - 9x^2 + 14 = 0
Замена: x^2=t
t^2 - 9t + 14 = 0
D = 81 - 56 = 25
х1 =
х2 =
x1 = 7 x2 = 2
x^2 = 7 и x^2 = 2
x = ±√7 x = ±
√2
Ответ: ±√7; ±√2
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Answers & Comments
Замена: x^2=t
t^2 + 35t - 36 = 0
a+b+c=0 ⇒ t1 = 1; t2 = c/a = 36
x^2 = 1 и x^2 = 36
x=±1 x=±6
Ответ: ±1, ±6
2) x^4 - 9x^2 + 14 = 0
Замена: x^2=t
t^2 - 9t + 14 = 0
D = 81 - 56 = 25
х1 =
х2 =
x1 = 7 x2 = 2
x^2 = 7 и x^2 = 2
x = ±√7 x = ±√2
Ответ: ±√7; ±√2