解方程组：x2y2+x2+y2=9;x2y+xy2-x-y=32为平方,..

来源：学生作业帮助网编辑：作业帮时间：2024/05/02 11:38:57

解方程组：x2y2+x2+y2=9;x2y+xy2-x-y=32为平方,..
解方程组：x2y2+x2+y2=9;x2y+xy2-x-y=3
2为平方,..

解方程组：x2y2+x2+y2=9;x2y+xy2-x-y=32为平方,..
x²y²+x²+y²=9
x²y²-2xy+1+x²+2xy+y²=10
(xy-1)²+(x+y)²=10
x²y+xy²-x-y=3
xy(x+y)-(x+y)=3
(x+y)(xy-1)=3>0
x+y与xy-1同号.
(x+y)²(xy-1)²=9
(x+y)²,(xy-1)²是方程m²-10m+9=0的两根.
m²-10m+9=0
(m-1)(m-9)=0
m=1或m=9
x+y=1 xy-1=3或x+y=-1 xy-1=-3
x+y=1 xy-1=3时,x+y=1 xy=4,x,y是方程m²-m+4=0的两根,方程无解.
x+y=-1 xy-1=-3时,x+y=-1 xy=-2 x,y是方程m²+m-2=0的两根.
m²+m-2=0
(m+1)(m-2)=0
m=-1或m=2
x=-1 y=2或x=2 y=-1.
综上,得
x=-1 y=2或x=2 y=-1.

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