已知x/3=y/4=z/5 求 分式y^2+z^2-x^2/x^2+z^2-y^2

来源:学生作业帮助网 编辑:六六作业网 时间:2024/12/27 00:56:41
已知x/3=y/4=z/5求分式y^2+z^2-x^2/x^2+z^2-y^2已知x/3=y/4=z/5求分式y^2+z^2-x^2/x^2+z^2-y^2已知x/3=y/4=z/5求分式y^2+z^

已知x/3=y/4=z/5 求 分式y^2+z^2-x^2/x^2+z^2-y^2
已知x/3=y/4=z/5 求 分式y^2+z^2-x^2/x^2+z^2-y^2

已知x/3=y/4=z/5 求 分式y^2+z^2-x^2/x^2+z^2-y^2
令a=x/3=y/4=z/5
x=3a,y=4a,z=5a
所以原式=(16a²+25a²-9a²)/(9a²+25a²-16a²)
=32a²/18a²
=16/9


根据题意可是x=3k,则y=4k z=5k,于是
(y^2+z^2-x^2)/(x^2+z^2-y^2)
=(16k²+25k²-9k²)/(9k²+25k²-16k²)
=32k²/18k²
=32/18
=16/9