已知 a²+ab-6b²=0,求a/b-b/a-(a²+b²)/ab的值
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已知 a²+ab-6b²=0,求a/b-b/a-(a²+b²)/ab的值
已知 a²+ab-6b²=0,求a/b-b/a-(a²+b²)/ab的值
已知 a²+ab-6b²=0,求a/b-b/a-(a²+b²)/ab的值
由已知:
a²+ab-6b²=0
1+b/a-6(b/a)²=0
6(b/a)²-b/a-1=0
[3(b/a)+1][2(b/a)-1]=0
解得:b/a=-1/3…………(1)
或者:b/a=1/2…………(2)
所求为:
a/b-b/a-(a²+b²)/ab
=(a²-b²)/ab-(a²+b²)/ab
=(a²-b²-a²-b²)/ab
=-2b²/ab
=-2b/a
将(1)、(2)代入,有:
有:a/b-b/a-(a²+b²)/ab=2/3,或者:a/b-b/a-(a²+b²)/ab=-1