若x+y+z≠0且2y+z/x=2x+y/z=2z+x/y=k,则k=?
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若x+y+z≠0且2y+z/x=2x+y/z=2z+x/y=k,则k=?
若x+y+z≠0且2y+z/x=2x+y/z=2z+x/y=k,则k=?
若x+y+z≠0且2y+z/x=2x+y/z=2z+x/y=k,则k=?
原等式写成:
(2y+z)/x=(2x+y)/z=(2z+x)/y=k
于是:
2y+z=kx,①
2x+y=kz,②
2z+x=ky,③
①+②+③,得
3(x+y+z)=k(x+y+z)
又∵x+y+z≠0
∴k=3
k=3x+3z+3y
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