If x =1 , y = 2 and z = 3 , then find `( x^2 + y^2 + z^2 )`

If x = 1, y = 2, z = 5 , then find the value of 3x – 2y + 4z.

If x = 1, y = 2 and z = 5 , find the value of 3x – 2y + z .

If (x + y)/2 = (y+z)/3 = (z + x)/4 , then find x : y: z .

If x=1, y=2, z=-1 then find the value of z^2-2xy(x-y)

If 2x = 3y = 4z, find x:y: z.

If x+y+z=6 and 3^(x)=5^(y)=15^(-z), then find x^(2)+y^(2)+z^(2)

Prove that |[x,y,z] , [x^2, y^2, z^2] , [yz, zx, xy]| = |[1,1,1] , [x^2, y^2, z^2] , [x^3, y^3, z^3]|

If x + y + z = xyz , prove that x(1 -y^(2)) (1- z^(2))+ y(1- z^(2))(1- x^(2)) +z(1-x^(2)) (1- y^(2)) = 4xyz .