已知x、y均为实数,且满足xy+x+y=17,x2y+xy2=66,则x4+x3y+x2y2+xy3+y4=_.

问题描述:

已知x、y均为实数,且满足xy+x+y=17,x2y+xy2=66,则x4+x3y+x2y2+xy3+y4=______.

x2y+xy2=xy(x+y)=66,设xy=m,x+y=n,由xy+x+y=17,得到m+n=17,由xy(x+y)=66,得到mn=66,∴m=6,n=11或m=11,n=6(舍去),∴xy=m=6,x+y=n=11,x2+y2=112-2×6=109,x2y2=36x4+y4=1092-36×2=11809x4+x3y+x2y...