x、y为正整数,并:xy+x+y=71,xxy+xyy=880,求xx+yy

问题描述:

x、y为正整数,并:xy+x+y=71,xxy+xyy=880,求xx+yy

xy+(x+y)=71
xxy+xyy=xy(x+y)=880
xy和x+y是方程m^2-71m+880=0的两根.
(m-55)(m-16)=0
m=55或m=16
x+y=16xy=55
xx+yy=(x+y)^2-2xy=256-110=146