If `x y z in R` are connected by `x+y+z=4 x^(2)+y^(2)+z^(2)=6` when `x` is minimum then value of `y` is

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^(2)+y^(2)+z^(2)=2(x-y-z)-3 Find the value of 2x-3y+4z

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 and z are three real numbers such that x+y+z=4 and x^(2)+y^(2)+z^(2)=6, then show that each of x,y and z lie in the closed interval [(2)/(3),2]

If x^(2)+y^(2)+z^(2)=1 , where x,y,z in R^(+) then greatest value of x^(2)y^(3)z^(4) is

If 4 x^(2) + 9y^(2) + z^(2) + 49 = 12 ( x+ y + z) , then what is the value of (4x + 9y - z) ?

If 2x+3y+6z=14 then the minimum value of x^(2)+y^(2)+z^(2) is