已知x/2=y/3=z/4,则(x^2-2y^2+3z^2)/(xy+2yz+3xz)的值是
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已知x/2=y/3=z/4,则(x^2-2y^2+3z^2)/(xy+2yz+3xz)的值是
为什么可以令x/2=y/3=z/4=t
等于x=2t,y=3t,z=4t
为什么可以令x/2=y/3=z/4=t
等于x=2t,y=3t,z=4t
![已知x/2=y/3=z/4,则(x^2-2y^2+3z^2)/(xy+2yz+3xz)的值是](/uploads/image/z/15731703-63-3.jpg?t=%E5%B7%B2%E7%9F%A5x%2F2%3Dy%2F3%3Dz%2F4%2C%E5%88%99%28x%5E2-2y%5E2%2B3z%5E2%29%2F%28xy%2B2yz%2B3xz%29%E7%9A%84%E5%80%BC%E6%98%AF)
因为 x/2=y/3=z/4 知道 x :y :z = 2 :3 :4
所以
令x/2=y/3=z/4=t
则x=2t,y=3t,z=4t
(x^2-2y^2+3z^2)/(xy+2yz+3xz)
=(4t^2-18t^2+48t^2)/(6t^2+24t^2+24t^2)
=34t^2/54t^2
=34/54
=17/27
所以
令x/2=y/3=z/4=t
则x=2t,y=3t,z=4t
(x^2-2y^2+3z^2)/(xy+2yz+3xz)
=(4t^2-18t^2+48t^2)/(6t^2+24t^2+24t^2)
=34t^2/54t^2
=34/54
=17/27
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