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nusja5934
@nusja5934
July 2022
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Розв'язати рівняння: x^4-5x^3+8x^2-5x+1=0.
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sedinalana
Verified answer
X³(x-1)-4x²(x-1)+4x(x-1)-(x-1)=0
(x-1)(x³-4x²+4x-1)=0
(x-1)[x²(x-1)-3x(x-1)+(x-1)]=0
(x-1)²(x²-3x+1)=0
x-1=0
x=1
x²-3x+1=0
D=9-4=5
x=(3-√5)/2 U x=(3+√5)/2
Ответ x={1;(3-√5)/2;(3=√5)/2}
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Answers & Comments
Verified answer
X³(x-1)-4x²(x-1)+4x(x-1)-(x-1)=0(x-1)(x³-4x²+4x-1)=0
(x-1)[x²(x-1)-3x(x-1)+(x-1)]=0
(x-1)²(x²-3x+1)=0
x-1=0
x=1
x²-3x+1=0
D=9-4=5
x=(3-√5)/2 U x=(3+√5)/2
Ответ x={1;(3-√5)/2;(3=√5)/2}