若x,y是正整数,且满足x(x+y)-y(x+y)=11求x+y的值

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

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

若x,y是正整数,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=6,y=5