由 --- 於 星期六 六月 14, 2003 1:32 am
x+y+z=1
let xx+yy+zz=m
let xy+yz+zx=b;m+2b=1; b=1/2-m/2; m=1-2b
let xyz=c
3-3c=xxx+yyy+zzz-3xyz
=(x+y+z)(m-b)
=1-3b
c=2/3+b
character eq:
rrr-rr+br-c=0
rrr-rr+br-(2/3+b)=0
rrr=rr-br+(2/3+b)
Q0=3
Q1=1
Q2=1-2b
Q3=3
Q4=3-b+2bb+2/3+b=11/3+2bb
Q5=5=8/3+2bb-3b+(1-2b)(2/3+b)=13/3-10b/3
b=-1/5
c=2/3-1/5=7/15
characteristic eq: 15rrr-15rr-3r-7=0
3 roots:
1.386845562
-0.193422781+0.54688452 i
-0.193422781+0.54688452 i