Question

已知a大于b大于0，且a的2次方+b的2次方=3ab求a+b除以a-b=？？？

Answer 1

a^2+b^2=3ab
(a+b)^2=5ab (a-b)^2=ab
a+b=根号5ab a-b=根号ab
a+b除以a-b=根号5

Answer 2

a²+b²=3ab
a²/b²+1=3a/b
a/b=(√5+3)/2或（-√5+3)/2
因为a>b>0 所以a/b>1
所以a/b=(√5+3)/2
(a+b)/(a-b)
=(a-b+2b)/(a-b)
=1+2b/(a-b)
=1+2/(a/b-1)
=√5

Answer 3

∵a^2+b^2=3ab
∴(a+b)^2=5ab
(a-b)^2=ab
(a+b)^2/(a-b)^2=5ab/ab=5
∵a大于b大于0
∴a+b>0,a-b>0
∴(a+b)/(a-b)=√5

Answer 4

有题意得a^2+b^2=3ab
(a-b)^2=a^2+b^2-2ab=ab
(a+b)^2=a^2+b^2+2ab=5ab
所以(a+b)^2/(a-b)^2=5
解得(a+b)/(a-b)为根号5