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palyan99
@palyan99
July 2022
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X^4=(x-2)^2
очень срочно.....
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zhenyaM2002
Verified answer
Х⁴= (х-2)²
x⁴=x²-4x+4
x⁴-x²+4x-4 =0
x²(x²-1)+ 4(x-1)=0
x²(x-1)(x+1) +4(x-1)=0
(x-1)(x² (x+1) +4) =0
(x-1)(x³+x²+4) =0
(x-1)(x²- 4 +x³+ 8)=0
(x-1)( (x-2)(x+2) + (x+2)(x²-2x+4))=0
(x-1)(x+2)(x-2+x²-2x+4)=0
(x-1)(x+2)(x²-x+2)=0
произведение = 0 , если один из множителей =0
x-1=0
x₁=1
x+2=0
x₂=-2
x²-x+2=0
D= (-1)²-4*1*2= 1-6 = -5 ; D<0 - нет корней
Ответ: х₁=1 ; х₂=-2
2 votes
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Answers & Comments
Verified answer
Х⁴= (х-2)²x⁴=x²-4x+4
x⁴-x²+4x-4 =0
x²(x²-1)+ 4(x-1)=0
x²(x-1)(x+1) +4(x-1)=0
(x-1)(x² (x+1) +4) =0
(x-1)(x³+x²+4) =0
(x-1)(x²- 4 +x³+ 8)=0
(x-1)( (x-2)(x+2) + (x+2)(x²-2x+4))=0
(x-1)(x+2)(x-2+x²-2x+4)=0
(x-1)(x+2)(x²-x+2)=0
произведение = 0 , если один из множителей =0
x-1=0
x₁=1
x+2=0
x₂=-2
x²-x+2=0
D= (-1)²-4*1*2= 1-6 = -5 ; D<0 - нет корней
Ответ: х₁=1 ; х₂=-2