已知实数x,y,z满足x/(y+z)+y/(z+x)+z/(x+y)=1,求x2/(y+z)+y2/(z+x)+z2/(x+y)的值

已知实数x,y,z满足x/(y+z)+y/(z+x)+z/(x+y)=1,求x2/(y+z)+y2/(z+x)+z2/(x+y)的值

题目
已知实数x,y,z满足x/(y+z)+y/(z+x)+z/(x+y)=1,求x2/(y+z)+y2/(z+x)+z2/(x+y)的值
答案
等于0.
x/(y+z)=1-[y/(z+x)+z/(x+y)]
y/(z+x)=1-[x/(y+z)+z/(x+y)]
z/(x+y)=1-[x/(y+z)+y/(z+x)]
x2/(y+z)+y2/(z+x)+z2/(x+y)
=x*[x/(y+z)]+y*[y/(z+x)]+z*[z/(x+y)]
=x*{1-[y/(z+x)+z/(x+y)]}+y*{1-[x/(y+z)+z/(x+y)]}+z*{1-[x/ (y+z)+y/(z+x)]}
=x-x*[y/(z+x)+z/(x+y)]+y-y*[x/(y+z)+z/(x+y)]+z-z*[x/(y+z)+y/(z+x)]
=x+y+z-[xy/(z+x)+xz/(x+y)+yx/(y+z)+yz/(x+y)+zx/(y+z)+zy/(z+x)]
=x+y+z-[xy/(z+x)+zy/(z+x)+yx/(y+z)+zx/(y+z)+xz/(x+y)+yz/(x+y)]
=x+y+x-[y(x+z)/(z+x)+x(y+z)/(y+z)+z(x+y)/(x+y)]
=x+y+z-(y+x+z)
=0
举一反三
已知函数f(x)=x,g(x)=alnx,a∈R.若曲线y=f(x)与曲线y=g(x)相交,且在交点处有相同的切线,求a的值和该切线方程.
我想写一篇关于奥巴马的演讲的文章,写哪一篇好呢?为什么好
奥巴马演讲不用看稿子.为什么中国领导演讲要看?
想找英语初三上学期的首字母填空练习……
英语翻译
最新试题
热门考点

超级试练试题库

© 2017-2019 超级试练试题库,All Rights Reserved.