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已知xy/(x+y)=6/5,xz/(x+z)=4/3,xyz/(xy+yz+xz)=12/13,则x+y+z=
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已知xy/(x+y)=6/5,xz/(x+z)=4/3,xyz/(xy+yz+xz)=12/13,则x+y+z=
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答案和解析
xy/(x+y)=6/5即5/6=(x+y)/xy=1/x+1/y
xz/(x+z)=4/3即3/4=(x+z)/xz=1/x+1/z
xyz/(xy+yz+xz)=12/13,13/12=1/x+1/y+1/z
前两式相加再减后式得5/6+3/4-13/12=1/x所以x=2
代入上式的y=3,z=4
所以x+y+z=9
xz/(x+z)=4/3即3/4=(x+z)/xz=1/x+1/z
xyz/(xy+yz+xz)=12/13,13/12=1/x+1/y+1/z
前两式相加再减后式得5/6+3/4-13/12=1/x所以x=2
代入上式的y=3,z=4
所以x+y+z=9
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