若x、y为正整数,且满足x(x+y)-y(x+y)=11,求x,y的值

若x、y为正整数,且满足x(x+y)-y(x+y)=11,求x,y的值
若x、y为正整数,且满足x(x+y)-y(x+y)=11,求x,y的值

若x、y为正整数,且满足x(x+y)-y(x+y)=11,求x,y的值
x(x+y)-y(x+y)=(x+y)(x-y)=11,又因为xy为正整数且11是质数,所以只能是11×1=11,所以x+y=11,x-y=1,解得x=6,y=5

X +1 + Y（X +1）= 6
（X +1）（Y +1）= 6
1.x的= Y = 1
2.X = 1 Y = 2