设a>b>0,a^2+b^2-6ab=0,则a+b⼀b-a的值等于多少

2025-04-15 12:44:13
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回答1:

a>b>0,则a/b>1

a²+b²-6ab=0
(a/b)²-6(a/b) +1=0
(a/b)²-6(a/b)+9=8
(a/b -3)²=8
a/b=3-2√2(小于1,舍去)或a/b=3+2√2
(a+b)/(b-a)
=(a/b +1)/(1- a/b)
=(3+2√2+1)/(1-3-2√2)
=-(2+√2)/(√2+1)
=-(2+√2)(√2-1)/[(√2+1)(√2-1)]
=-√2/(2-1)
=-√2
(a+b)/(b-a)的值为-√2