已知x:y:z=1:2:3 求分式(x^2+y^2+z^2)/(xy-2yz+3xz)的值

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已知x:y:z=1:2:3 求分式(x^2+y^2+z^2)/(xy-2yz+3xz)的值

已知x:y:z=1:2:3 求分式(x^2+y^2+z^2)/(xy-2yz+3xz)的值
已知x:y:z=1:2:3 求分式(x^2+y^2+z^2)/(xy-2yz+3xz)的值

已知x:y:z=1:2:3 求分式(x^2+y^2+z^2)/(xy-2yz+3xz)的值
由题可知:
y=2x,
z=3x
故:
(x^2+y^2+z^2)/(xy-2yz+3xz)
=(x^2+4x^2+9x^2)/(x*2x-2*2x*3x+3x*3x)
=14x^2/(2x^2-12x^2+9x^2)
=-14x^2/x^2
=-14

设x=k,y=2k,z=3k
(x^2+y^2+z^2)/(xy-2yz+3xz)
=(k^2+4k^2+9k^2)/(2k^2-12k^2+9k^2)
=14k^2/(-k^2)
=-14

-14
设X=k,y=2k,z=3k代进去算