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xyz不等于0,x+y+z=0a=x/(y+z)b=y/(z+x)c=z/(x+y)求a/(a-1)+b/(b-1)+c/(c-1)的值
题目详情
xyz不等于0,x+y+z=0
a=x/(y+z)
b=y/(z+x)
c=z/(x+y)
求 a/(a-1)+b/(b-1)+c/(c-1)的值
a=x/(y+z)
b=y/(z+x)
c=z/(x+y)
求 a/(a-1)+b/(b-1)+c/(c-1)的值
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答案和解析
由xyz不等于0,x+y+z=0得：
X+Y=-Z；Y+Z=-X；X+Z=-Y
即a=X/-X=-1;b=Y/-Y=-1;c=Z/-Z=-1
所以原式=-1/-2+-1/-2+-1/-2=3/2
X+Y=-Z；Y+Z=-X；X+Z=-Y
即a=X/-X=-1;b=Y/-Y=-1;c=Z/-Z=-1
所以原式=-1/-2+-1/-2+-1/-2=3/2
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