已知x/2=y/3=z/4,那么(x^2-2y^2+3z^2)/xy+2yz+3zx的值是

来源:学生作业帮助网 编辑:作业帮 时间:2024/05/09 10:48:23
已知x/2=y/3=z/4,那么(x^2-2y^2+3z^2)/xy+2yz+3zx的值是

已知x/2=y/3=z/4,那么(x^2-2y^2+3z^2)/xy+2yz+3zx的值是
已知x/2=y/3=z/4,那么(x^2-2y^2+3z^2)/xy+2yz+3zx的值是

已知x/2=y/3=z/4,那么(x^2-2y^2+3z^2)/xy+2yz+3zx的值是
设x/2=y/3=z/4=k
则:x=2k;y=3k;z=4k
(x^2-2y^2+3z^2)/xy+2yz+3zx
=(4k²-18k²+48k²)/(6k²+24k²+24k²)
=34/54
=17/27


令x/2=y/3=z/4=t,则x=2t,y=3t,z=4t
(x²-2y²+3z²)/(xy+2yz+3zx)
=(4t²-18t²+48t²)/(6t²+24t²+24t²)
=34t²/(54t²)
=17/27

x=2,y=3,z=4直接带路省的设了,

可以取X=2,Y=3,Z=4.那么x^2-2y^2+3z^2=2*2-2*3*3+3*4*4=34, xy+2yz+3zx=2*3+2*3*4+3*4*2=54,结果就是34/54=17/28