Question

设a小于b小于0，a平方+b平方=4ab，则a+b/a-b的值=？

请写清步骤

Answer 1

因为a^2+b^2=4ab
所以（a-b)^2=2ab,(a+b)^2=6ab
又因为a<b<0
所以a-b=负根号2，a+b=负根号6
所以a+b/a-b=根号3

Answer 2

a<b<0

a^2+b^2=4ab
a^2+2ab+b^2=6ab
(a+b)^2=6ab
-(a+b)=√(6ab)
a+b=-√(6ab)

a^2+b^2=4ab
a^2-2ab+b^2=2ab
(a-b)^2=2ab
-(a-b)=√(2ab)
a-b=-√(2ab)

(a+b)/(a-b)
=[-√(6ab)]/[-√(2ab)]
=√6/√2
=√3