3S^4+18S^3+30S^2+18S+3=0没分了,

Question

3S^4+18S^3+30S^2+18S+3=0 没分了,

Answer 1

3S^4+18S^3+30S^2+18S+3=0
S^4+6S^3+10S^2+6S+1=0
S^4+S^3+5S^3+5S^2+5S^2+5S+S+1=0
S^3(S+1)+5S^2(S+1)+5S(S+1)+(S+1)=0
(S+1)(S^3+5S^2+5S+1)=0
S1=-1
S^3+5S^2+5S+1=0
S^3+S^2+4S^2+4S+S+1=0
(S^3+S^2)+(4S^2+4S)+(S+1)=0
S^2(S+1)+4S(S+1)+(S+1)=0
(S+1)(S^2+4S+1)=0
S2=-1
S^2+4S+1=0
S^2+4S+4=3
(S+2)^2=3
S+2=±√3
S=-2±√3
S3=-2+√3
S4=-2-√3