[" If "x^(2)=y+z,y^(2)=z+x,z^(2)=x+y," then the value of "],[(1)/(x+1)+(1)/(y+1)+(1)/(z+1)" is: "]

If (x+y-z)^(2) +(y+z-x)^(2) +(z+x-y)^(2)=0 then what is the value of x+y+z ?

If x , y, z in R, x + y + z= 4 and x^(2) + y^(2) + z^(2) = 6 , then the maximum possible value of z is

If x+y+z=0 then what is the value of (1)/(x^(2)+y^(2)-z^(2)) +(1)/(y^(2)+z^(2)-x^(2)) +(1)/(z^(2)+x^(2)-y^(2)) ?

Let A=[(0, 2y,z),(x,y,-z),(x,-y,z)] such that A^(T)A=I , then the value of x^(2)+y^(2)+z^(2) is