已知实数x,y,z满足,x+1/y=4,y+1/z=1,z+1/x=7/3,求xyz的值

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已知实数x,y,z满足,x+1/y=4,y+1/z=1,z+1/x=7/3,求xyz的值
已知实数x,y,z满足,x+1/y=4,y+1/z=1,z+1/x=7/3,求xyz的值

已知实数x,y,z满足,x+1/y=4,y+1/z=1,z+1/x=7/3,求xyz的值
三式相加:x+y+z+1/x+1/y+1/z=22/3
三式相乘:xyz+y+x+1/z+z+1/x+1/y+1/xyz=28/3
将1式代入2式
得到xyz+22/3+1/xyz=28/3
即:xyz+1/xyz=2.所以xyz=1

1

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