设a>b>0,a^2+b^2=6ab,则(a+b)/(a-b)的值等于＿_数学解答

设a>b>0,a^2+b^2=6ab,则(a+b)/(a-b)的值等于＿

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解答

a^2+b^2=6ab
(a+b)^2=8ab
(a-b)^2=4ab
a>b>0
a+b=√8ab
a-b=√4ab
(a+b)/(a-b)
=√8ab/√4ab
=√2