集合A={x∈R|x=a+b根号2,a∈Z,b∈Z} 判断元素x与集合A的关系,

A={x∈R|x=a+b√2,a∈Z,b∈Z}
x1∈A,x2∈A
x1=a1+b1*√2,x2=a2+b2*√2
(1)
X=x1+x2=(a1+a2)+(b1+b2)*√2
X∈A
(2)
X=x1/x2=(a1+b1*√2)/(a2+b2*√2)
=[(a1*a2-2*b1*b2)/(a2^2-2*b2^2)]+[(a2*b1-a1*b2)/(a2^2-2*b2^2)]*√2
(a1*a2-2*b1*b2)/(a2^2-2*b2^2)和(a2*b1-a1*b2)/(a2^2-2*b2^2)不一定是整数
X不一定∈A