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x+y+z=0,xyz=1/5,求1/x+1/y+1/z的值
题目详情
x+y+z=0,
xyz=1/5,
求1/x+1/y+1/z的值
xyz=1/5,
求1/x+1/y+1/z的值
▼优质解答
答案和解析
1/x+1/y+1/z=y/xy+x/xy+1/z
=(x+y)/xy+1/z
=[(x+y)*z+xy]/xyz
已知x+y+z=0 x+y=-z
xyz=1/5 xy=1/5z 所以(x+y)*z+xy=-z*z+1/5z
1/x+1/y+1/z=(-z*z+1/5z)*5
感觉还差一个条件一样,我只能帮你换成只剩一元Z的值了
=(x+y)/xy+1/z
=[(x+y)*z+xy]/xyz
已知x+y+z=0 x+y=-z
xyz=1/5 xy=1/5z 所以(x+y)*z+xy=-z*z+1/5z
1/x+1/y+1/z=(-z*z+1/5z)*5
感觉还差一个条件一样,我只能帮你换成只剩一元Z的值了
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