x1+x2+x3+x4=0,x2+x3+x4+x5=0,x1+2 x2+3 x3=2,x2+2 x3+3 x4=-2,x3+2 x4+3 x5=2求法,

题目

x1+x2+x3+x4=0,x2+x3+x4+x5=0,x1+2 x2+3 x3=2,x2+2 x3+3 x4=-2,x3+2 x4+3 x5=2求法,

答案

x1+x2+x3+x4=0...(1)
x2+x3+x4+x5=0...(2)
x1+2 x2+3 x3=2...(3)
x2+2 x3+3 x4=-2...(4)
x3+2 x4+3 x5=2...(5)
(1)-(2):x1=x5
(3)-(4):x1+x2+x3-3 x4=4
x1+x2+x3+x4=4+4 x4=0
x4=-1
(4)-(5):x2+x3+x4-3 x5=-4
x2+x3+x4+x5=-4+4 x5=0
x5=1
x1=1
(2):x2+x3=0
(3):1+2 x2+3 x3=2
(2)(3):x3=1 x2=-1
所以 x1=1,x2=-1,x3=1,x4=-1,x5=1