X^5+2x^4-3x^3-3x^2+x+1=0
x^4 (x+1) - 3x^2 (x+1) + (x+1)=0
(x+1)(x^4 - 3x^2+1)=0
x+1=0 --> x= -1
x^4 - 3x^2+1=0 --> D=9-4=5 -->
x^2=(3+sqrt5)/2 --> x=sqrt((3+sqrt5)/2), x= -sqrt((3+sqrt5)/2)
x^2=(3-sqrt5)/2 --> x=sqrt((3-sqrt5)/2), x= -sqrt((3-sqrt5)/2)
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Answers & Comments
x^4 (x+1) - 3x^2 (x+1) + (x+1)=0
(x+1)(x^4 - 3x^2+1)=0
x+1=0 --> x= -1
x^4 - 3x^2+1=0 --> D=9-4=5 -->
x^2=(3+sqrt5)/2 --> x=sqrt((3+sqrt5)/2), x= -sqrt((3+sqrt5)/2)
x^2=(3-sqrt5)/2 --> x=sqrt((3-sqrt5)/2), x= -sqrt((3-sqrt5)/2)