求解五元方程组（平方不好打,我就写成xx,yy,zz的形式）yz+2ux+v=zx+2uy+v=xy+2uz+v=0;xx+yy+zz-1=x+y+z=0

Question

求解五元方程组（平方不好打,我就写成xx,yy,zz的形式）
yz+2ux+v=zx+2uy+v=xy+2uz+v=0;
xx+yy+zz-1=x+y+z=0

Answer 1

一共六组解,下边每一横行依次为：u,v,x,y,z
[ 6^(1/2)/12,1/6,6^(1/2)/6,6^(1/2)/6,-6^(1/2)/3]
[ -6^(1/2)/12,1/6,-6^(1/2)/6,-6^(1/2)/6,6^(1/2)/3]
[ 6^(1/2)/12,1/6,-6^(1/2)/3,6^(1/2)/6,6^(1/2)/6]
[ 6^(1/2)/12,1/6,6^(1/2)/6,-6^(1/2)/3,6^(1/2)/6]
[ -6^(1/2)/12,1/6,-6^(1/2)/6,6^(1/2)/3,-6^(1/2)/6]
[ -6^(1/2)/12,1/6,6^(1/2)/3,-6^(1/2)/6,-6^(1/2)/6]