若a,b满足(a/b)/(b/a)=2,则(a^2+ab+b^2)/(a^2+4ab+b^2)的值是?

来源:学生作业帮助网 编辑:作业帮 时间:2024/05/04 04:40:34
若a,b满足(a/b)/(b/a)=2,则(a^2+ab+b^2)/(a^2+4ab+b^2)的值是?

若a,b满足(a/b)/(b/a)=2,则(a^2+ab+b^2)/(a^2+4ab+b^2)的值是?
若a,b满足(a/b)/(b/a)=2,则(a^2+ab+b^2)/(a^2+4ab+b^2)的值是?

若a,b满足(a/b)/(b/a)=2,则(a^2+ab+b^2)/(a^2+4ab+b^2)的值是?
(a/b)/(b/a)=2,
(a/b)*(a/b)=2
a^2=2b^2
则(a^2+ab+b^2)/(a^2+4ab+b^2)
=(2b^2+ab+b^2)/(2b^2+4ab+b^2)
=(3b^2+ab)/(3b^2+4ab)
(1):a=根号2*b:
=(3b^2+根号2*b^2)/(3b^2+4根号2*b^2)
=(3+根号2)/(3+4根号2)
(2)a=-根号2*b
=(3-根号2)/(3+4根号2)
(过程同上)