若x/2=y/3=z/4,求(xy+yz+zx)/(x²+y²+z²)的值.
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若x/2=y/3=z/4,求(xy+yz+zx)/(x²+y²+z²)的值.若x/2=y/3=z/4,求(xy+yz+zx)/(x²+y²+z
若x/2=y/3=z/4,求(xy+yz+zx)/(x²+y²+z²)的值.
若x/2=y/3=z/4,求(xy+yz+zx)/(x²+y²+z²)的值.
若x/2=y/3=z/4,求(xy+yz+zx)/(x²+y²+z²)的值.
x/2=y/3=z/4
所以
y=3x/2
z=2x
所以原式=(3x²/2+3x²+2x²)/(x²+9x²/4+4x²)
=(13x²/2)/(29x²/4)
=26/29
设x/2=y/3=z/4=t
∴x=2t,y=3t,z=4t
∴(xy+yz+zx)/(x²+y²+z²)
=(6t²+12t²+8t²)/(4t²+9t²+16t²)
=26t²/29t²
=26/29
这个比较简单,建立已知和求解之间的联系就可以了/
设X/2=Y/3=Z/4=m
则x=2m,y=3m,z=4m
然后分别代入式子化简就可以了。
最后m可以消掉。
用特殊值带 最简单通用了
也可以x=2k,y=3k,z=4k带入可得
26/29
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