已知x/3=y/1+z/2,求(2x²-2y²+5z²)/(xy+yz+xz)的值

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已知x/3=y/1+z/2,求(2x²-2y²+5z²)/(xy+yz+xz)的值
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已知x/3=y/1+z/2,求(2x²-2y²+5z²)/(xy+yz+xz)的值
已知x/3=y/1+z/2,求(2x²-2y²+5z²)/(xy+yz+xz)的值

已知x/3=y/1+z/2,求(2x²-2y²+5z²)/(xy+yz+xz)的值
设3/x=1/y/=2/z=k,则,x=3/k,y=1/k,z=2/k
代人,得,
(2x²-2y²+5z²)/(xy+yz+xz)
=(18/k²-2/k²+20/k²)/(3/k²+2/k²+6/k²)
=(36/k²)/(11/k²)
=36/11

设x/3=2,y/1=z/2=1,则 x=6,y=1,z=2,带入右边=(2*36-2*1+5*4)/(6*1+1*2+2*6)
=(72-2+20)/(6+2+12)=90/20=4.5