yalovey
幼苗
共回答了13个问题采纳率:92.3% 举报
设x1=a+b√2,x2=c+d√2,(a,b,c,d∈Q),则x1,x2∈F
x1+x2=a+b√2+c+d√2 =(a+c)+(b+d)√2∈F
x1-x2=a+b√2-(c+d√2) =(a-c)+(b-d)√2∈F
x1*x2=(a+b√2)(c+d√2)=(ac+2bd)+(ad+bc)√2∈F
x1/x2=(a+b√2)/(c+d√2)
=(a+b√2)(c-d√2)/[(c+d√2)(c-d√2)]
=[(ac-2bd)+(bc-ad)√2]/(c^2-2d^2)
=(ac-2bd)/(c^2-2d^2)+[(bc-ad) /(c^2-2d^2)]√2∈F
所以数集F是数域
1年前
2