If x+y+z=0 , then (x+y)(y+z)(z+x) is equal :

If x,y , z are in A.P then (x-y)/(y-z) is equal to _________-

The value of ( x-y ) ( x + y ) + ( y -z ) ( y + z ) + (z-x ) (z + x ) is equal to

If x + y + z = 0 , then what is (y+z-x)^(3) + (z+x-y)^(3) + (x+y-z)^(3) equal to ?

If the system of equations, 2x + 3y-z = 0, x + ky -2z = 0 " and " 2x-y+z = 0 has a non-trivial solution (x, y, z), then (x)/(y) + (y)/(z) + (z)/(x) + k is equal to

If the system of equations, 2x + 3y-z = 0, x + ky -2z = 0 " and " 2x-y+z = 0 has a non-trivial solution (x, y, z), then (x)/(y) + (y)/(z) + (z)/(x) + k is equal to

If x+y+z=0 , then [(y-z-x)//2]^(3)+[(z-x-y)//2]^(3)+[(x-y-z)//2]^(3) equals

If x/(x+2y+z) = y/(y+2z+x) = z/(z+2x +y) and x+y+z !=0 , then show that each ratio is equal to 1/4 .