已知x+y+z=6,1/(x-1)+1/(y-2)+1/(z-3)=0,求(x-1)^2+(y-2)^2+(z-3)^2的值

来源：学生作业帮助网编辑：六六作业网时间：2024/05/09 03:32:06

已知x+y+z=6,1/(x-1)+1/(y-2)+1/(z-3)=0,求(x-1)^2+(y-2)^2+(z-3)^2的值已知x+y+z=6,1/(x-1)+1/(y-2)+1/(z-3)=0,求(

已知x+y+z=6,1/(x-1)+1/(y-2)+1/(z-3)=0,求(x-1)^2+(y-2)^2+(z-3)^2的值
已知x+y+z=6,1/(x-1)+1/(y-2)+1/(z-3)=0,求(x-1)^2+(y-2)^2+(z-3)^2的值

已知x+y+z=6,1/(x-1)+1/(y-2)+1/(z-3)=0,求(x-1)^2+(y-2)^2+(z-3)^2的值
为了方便输入,设x-1=a,y-2=b,z-3=c
由x+y+z=6,得a+b+c=0
由1/a+1/b+1/c=0得bc+ac+ab=0
(a+b+c)^2=a^2+b^2+c^2+2(bc+ac+ab)
可得所求值为(x-1)^2+(y-2)^2+(z-3)^2=a^2+b^2+c^2=0.

x+y+z=6，得到(x－1)＋(y－2)＋(z－3)=0，且1/(x-1)+1/(y-2)+1/(z-3)=0，等介于a＋b＋c=0且1/a＋1/b＋1/c=0，由第二个去分母得到：ab＋bc＋ca=0，第一个平方后再减去第二个的2倍，得：a²＋b²＋c²=0。
题目好像有问题啊。。

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)=? 已知x:y=3:5 y:z=6:1,求x:y:z( ):( ):( ) 已知x:：y：z=3：4：5,(1)求x+y分之z的值；（2）若x+y+z=6,求x,y,z. 已知x,y,z满足x+y+2z=1,x²+y²+6z+1.5=0,求x,y,z的值已知实数x y z满足x/(x+1)=y/(y+2)=z/(z+3)=(x+y+z)/3,求x+y+z的值已知实数x y z满足x/(x+1)=y/(y+2)=z/(z+3)=(x+y+z)/3,求x+y+z的值已知实数X.Y.Z满足(Y+Z)分之X+(Z+X)分之Y+(X+Y)分之Z=1,则(Y+Z)分之X平方+(Z+X)分之Y平方+(X+Y)分之Z平方的值为（）已知x,y,z>0,xyz(x+y+z)=1,求证（x+y）(x+z)>=2 已知x-2y=3,x-y+z=4,x+6y+2z=-1,求x,y,z分别为多少? 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 + y²/z+x + z²/x+y的值.3Q 已知x+2y-3z=0,5x-6y+7z=1;则x:y:z=?把“5z-6y+7z=1”改成“5x-6y+7z=0” 已知x,y,z满足 -------------- + --------------- + ------------- = 1 y+z x+z x+yx•x y•y z•z求 ------------ + ------------ + -------------- = y+z x+z x+y 已知3x=4Y,5Y=6Z,求 (1)x:y:z;（2）x+y/y+z.请说明道理，已知3x=4Y,5Y=6Z,求 (1)x:y:z;(2)x+y/y+z 帮忙解道题 ,已知x+1/y=y+1/z=z+1/x ,证明x+y+z=1 已知；根号x+根号y-1+根号z-2=1/2(x+y+z),求x、y、z 已知{x：y：z=1：2：3,x+y+z=12,求x、y、z的值已知｛2x-y-z=0,3x-9y+z=0求1,x:y:z