初三奥数题若实数x,y,z满足:xy/x+2y=1,zy/y+2z=2,zx/z+2x=3,则x=
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依题意知:x≠0,y≠0,z≠0
xy/(x+2y)=1 =>xy=x+2y -----①
zy/(y+2z)=2 =>zy=2(y+2z) =>z(y-4)=2y -----② 显然y≠4
zx/(z+2x)=3 =>zx=3(z+2x) =>z(x-3)=6x -----③ 显然x≠3
②/③得:(y-4)/(x-3)=y/(3x)
=> 2xy=12x-3y ------④
2*①-④得:10x=7y => y=10x/7 ----⑤
将⑤代入①解得:x=27/10
【注:将x=27/10代入⑤可求y,代入③可求z】
xy/(x+2y)=1 =>xy=x+2y -----①
zy/(y+2z)=2 =>zy=2(y+2z) =>z(y-4)=2y -----② 显然y≠4
zx/(z+2x)=3 =>zx=3(z+2x) =>z(x-3)=6x -----③ 显然x≠3
②/③得:(y-4)/(x-3)=y/(3x)
=> 2xy=12x-3y ------④
2*①-④得:10x=7y => y=10x/7 ----⑤
将⑤代入①解得:x=27/10
【注:将x=27/10代入⑤可求y,代入③可求z】
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