已知 x/(y+z)+y/(z+x)+z/(x+y)=1
来源:学生作业帮 编辑:拍题作业网作业帮 分类:数学作业 时间:2024/03/29 08:46:12
已知 x/(y+z)+y/(z+x)+z/(x+y)=1
求 (x*x)/(y+z)+(y*y)/(x+z)+(z*z)/(x+y)=?
求 (x*x)/(y+z)+(y*y)/(x+z)+(z*z)/(x+y)=?
因为x/y+z + y/z+x +z/x+y=1
所以x/y+z=1-y/z+x-z/x+y,两边同乘以x
得x^2/y+z=x-xy/z+x-xz/x+y
同理y^2/x+z=y-xy/z+y-yz/x+y,z^2=z-xz/y+z-yz/x+z
所以原式=x+y+z-(xy+zy)/x+z-(xz+yz)/x+y-(yx+zx)/y+z
=x+y+z-y-z-x
=0
所以x/y+z=1-y/z+x-z/x+y,两边同乘以x
得x^2/y+z=x-xy/z+x-xz/x+y
同理y^2/x+z=y-xy/z+y-yz/x+y,z^2=z-xz/y+z-yz/x+z
所以原式=x+y+z-(xy+zy)/x+z-(xz+yz)/x+y-(yx+zx)/y+z
=x+y+z-y-z-x
=0
已知x,y,z满足x/(y+z)+y/(z+x)+z/(x+y)=1,求代数式x2/(y+z)+y2/(x+z)+z2/
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/(
已知 x/(y+z)+y/(z+x)+z/(x+y)=1
(x+y-z)(x-y+z)=
已知 x,y,z都是正实数,且 x+y+z=xyz 证明 (y+x)/z+(y+z)/x+(z+x)/y≥2(1/x+1
已知x+y-z/z=x-y+z/y=-x+y+z/x,且xyz不等于0,求分式[(x+y)(x+z)(y+z)]/xyz
已知:(x+y-z)/z=(x-y+z)/y+(y+z-x)/x,且xyz≠0,求代数式[(x+y)(y+z)(x+z)
X+Y+Z=?
一条分式数学题已知x y z满足x/x+y + y/z+x + z/x+y =1,求x²/x+y + y&su
1.已知x,y,z满足2│x-y│+(根号2y-z)+z平方-z+(1/4)=0,求x,y,z值.
已知x、y、z满足|4x-4y+1|+152y+z+(z−12)
x+y+z=1 求xyz/(x+y)(y+z)(z+x)的最大值