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Umnik1234
@Umnik1234
July 2022
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(x-1)^4-2(x-1)^2-3=0
решите уравнение
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miron2077
Verified answer
Обозначим (х-1)²=у
у²-2у-3=0
у₁=
2+√(4+12)
=
2+4
= 3
2 2
у₂=
2-√(4+12)
=
2-4
=-1
2 2
х²-2х+1=3
х²-2х-2=0
х₁=
2+√(4+8)
=
2+2√3
= 1+√3
2 2
х₂=
2-√(4+8)
=
2-2√3
= 1-√3
2 2
х²-2х+1=-1
х²-2х+2=0
х₃=
2+√(4-8)
дискриминант меньше 0, решений нет
2
Уравнение имеет два корня х₁ и х₂
15 votes
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Answers & Comments
Verified answer
Обозначим (х-1)²=уу²-2у-3=0
у₁=2+√(4+12) =2+4 = 3
2 2
у₂=2-√(4+12) =2-4 =-1
2 2
х²-2х+1=3
х²-2х-2=0
х₁=2+√(4+8) = 2+2√3 = 1+√3
2 2
х₂=2-√(4+8) = 2-2√3 = 1-√3
2 2
х²-2х+1=-1
х²-2х+2=0
х₃=2+√(4-8) дискриминант меньше 0, решений нет
2
Уравнение имеет два корня х₁ и х₂