设Q表示有理数集,集合A=|a+b根号2|a,b属于Q|.

问题描述:

设Q表示有理数集,集合A=|a+b根号2|a,b属于Q|.
(1)如果x1,x2属于A,求证:x1+x2属于A,x1*x2属于A
(2)于任意的y1,y2属于A,且y2不等于0,是否一定有y1/y2 属于A,试说明理由

x1 = a + b√2,x2 = c + d√2,则(1) x1 + x2 = (a+b) + (c+d)√2 ∈ A;x1x2 = (ac+2bd) + (ad+bc)√2 ∈ A.(2)x1/x2 = (a+b√2)/(c+d√2) = (a+b√2)(c-d√2)/(c&sup2-2d&sup2)= (ac-2bd)/(c&sup2-2d&sup2) + [(bc-...