请大家想一想一道证明题,急···

请大家想一想一道证明题,急···
请大家想一想一道证明题,急···

请大家想一想一道证明题,急···
令c = 根号2
因为x1∈A 所以假设 x1 = a1 + b1 * c (a1∈Z,b1∈Z)
同理假设 x2 = a2 + b2 * c (a2∈Z,b2∈Z)
x1 + x2 = ( a1 + a2 ) + (b1 + b2) * c (因为a1 + a2 ∈ Z 且 b1 + b2 ∈ Z 所以 x1 + x2 ∈ A)
x1 * x2 = (a1 + b1 * c ) * (a2 + b2 * c) = a1 * a2 + a1 * b2 * c + b1 * c * a2 + 2 * b1 * b2
= ( a1 * a2 + 2 * b1 * b2 ) + ( a1 * b2 + b1 * a2 ) * c (因为a1 * a2 + 2 * b1 * b2 ∈ Z 且 a1 * b2 + b1 * a2 ∈ Z 所以 x1 * x2 ∈ A)