解方程组：x+y+xy=11x2y+xy2=30,快
问题描述：
解方程组：x+y+xy=11x2y+xy2=30,快
答
设x+y=m,xy=n,则原式可化为
m+n=11
mn=30
m=11-n
(11-n)n=30
n^2-11n+30=0
(n-5)(n-6)=0
n=5,n=6
当n=5时,x+y=6,xy=5
x=6-y
y(6-y)=5
y^2-6y+5=0
(y-1)(y-5)=0
y=1,x=5
y=5,x=1
当n=6时,x+y=5,xy=6
x=5-y
y(5-y)=6
y^2-5y+6=0
(y-2)(y-3)=0
y=2,x=3
y=3,x=2