If `x,y,z, in R ` and independent of each other, then the range of `k=|x|+|y^3|+|z^5|+1/(|x|)+1/(|y^3|)+1/(|z^5|)` is

If x+y+z=1,\ x y+y z+z x=-1\ \ a n d\ x y z=-1, find the value of x^3+y^3+z^3

If x+y+z=1,x y+y z+z x=-1 and x y z=-1, find the value of x^3+y^3+z^3dot

If x : y = 1 : 3, y :z = 5 :k, z : t = 2:5 and t:x = 3:4 , then what is the value of k ?

If x, y, z in R are such that they satisfy x + y + z = 1 and tan^(-1)x+tan^(-1)y+tan^(-1)z=(pi)/(4) , then the value of |x^(3)+y^(3)+z^(3)-3| is

If x, y, z in R are such that they satisfy x + y + z = 1 and tan^(-1)x+tan^(-1)y+tan^(-1)z=(pi)/(4) , then the value of |x^(3)+y^(3)+z^(3)-3| is

If x, y, z in R are such that they satisfy x + y + z = 1 and tan^(-1)x+tan^(-1)y+tan^(-1)z=(pi)/(4) , then the value of |x^(3)+y^(3)+z^(3)-3| is

If the lines (x -1)/(-3) = (x - 2)/(2k) = (z - 3)/(2) and (x - 1)/(3k ) = (y -1)/(1) = (z - 6)/(-5) are perpendicular to each other, then the value of k is ,

If the lines (x-1)/k=(y-3)/2=(2-z)/-5 and (x-1)/3=(2-y)/-4=z/k are perpendicular to each other, then what is the value of k ?

If |(x, x^2, x^3 +1), (y, y^2, y^3+1), (z, z^2, z^3+1)| = 0 and x ,y and z are not equal to any other, prove that, xyz = -1