Question

设a大于b大于0,a^2+b^2-6ab=0，则(a+b)/(a-b)的值等于多少

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Answer 1

设a大于b大于0,a^2+b^2-6ab=0
a²+b²-2ab=4ab
(a-b)²=4ab
(a+b)²=a²+b²+2ab=(a-b)²+4ab=8ab
(a+b)²÷(a-b)²=8ab÷4ab=2
(a+b)／(a-b)=√2

Answer 2

a^2+b^2-6ab=0
(a+3b)(a-2b)=0
a+3b=0或a-2b=0
∵a＞b＞0
∴a=2b＞0
∴(a+b)/(a-b)
=(2b+b)/(2b-b)
=3

Answer 3

(a+b)^2=8ab
(a-b)^2=4ab
a>b>0
(a+b)/(a-b)=sqr(2)(根号2)