已知a2+b2=6ab且a>b>0,则a+b/a-b的值为

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已知a2+b2=6ab且a>b>0,则a+b/a-b的值为

已知a2+b2=6ab且a>b>0,则a+b/a-b的值为
已知a2+b2=6ab且a>b>0,则a+b/a-b的值为

已知a2+b2=6ab且a>b>0,则a+b/a-b的值为
因为a>b>0
所以
a+b/a-b
=√[(a+b)²/(a-b)²]
=√[(a²+2ab+b²)/(a²-2ab+b²)]
=√[(6ab+2ab)/(6ab-2ab)]
=√(8ab/4ab)
=√2

a>b>0
a2+b2=6ab
a^2-2ab+b^2=4ab
(a-b)^2=4ab
a-b=根号(4ab)
a2+b2=6ab
a^2+2ab+b^2=8ab
(a+b)^2=8ab
a+b=根号(8ab)
(a+b)/ (a-b)
= 根号(8ab) /根号(4ab)
=根号2

a>b>0
a2+b2=6ab
a^2-2ab+b^2=4ab
(a-b)^2=4ab
a-b=根号(4ab)
a2+b2=6ab
a^2+2ab+b^2=8ab
(a+b)^2=8ab
a+b=根号(8ab)
(a+b)/ (a-b)
= 根号(8ab) /根号(4ab)
=根号2

a²+b²=6ab
(a/b)² - 6(a/b) + 1 =0
a/b = 3±2√2
(a+b)/(a-b) = (a/b + 1)/(a/b - 1) = ±√2