If `2x-3y-z=0` and `x+3y-14z=0` ,then value of `(x^(2)+3xy)/(y^(2)+z^(2))` is

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

If x + y + z = 0 , then the value of (x^2)/(yz) + (y^2)/(zx) + (z^2)/(xy) is:

If (x_(0), y_(0), z_(0)) is any solution of the system of equations 2x-y-z=1, -x-y+2z=1 and x-2y+z=2 , then the value of (x_(0)^(2)-y_(0)^(2)+1)/(z_(0)) (where, z_(0) ne 0 ) is

If x^(3)+y^(3)+z^(3)=3xyz and x+y+z=0 , then the value of ((x+y)^(2))/(xy)+((y+z)^(2))/(yz)+((z+x)^(2))/(zx) is

If x+y+z=0 then what is the value of (x^2)/(3z)+(y^3)/(3xz)+(z^2)/(3x) ?

Let 2x+3y+4z=9,x,y,z>0 then the maximum value of (1+x)^(2)(2+y)^(3)(4+z)^(4) is