Question

一道数学题，求过程!谢谢大家了~~

已知x和y是正整数,并且满足条件xy+x+y=71,x方y+xy方=880,求x方+y方的值

Answer 1

880=xy(x+y)
=xy(71-xy)
(xy)2-71xy+880=0
(xy-16)(xy-55)=0

880=xy(x+y)
=(x+y)(71-x-y)
同理有x+y=16或x+y=55

又∵xy+x+y=71
∴x=11,y=5或x=5,y=11
∴?=121+25=146