If `x^(2) + y^(2) + z^(2) - xy- yz - zx = 0`, prove that : `x= y = z`

If x,y, z and w are non-zero real numbers and x^(2) + 5y^(2) + 5z^2+4w^(2) - 4xy - 4yz - 4zw = 0 , then x, y, z,w are in

If x,y and z are three different numbers, then prove that : x^(2) + y^(2) + z^(2)- xy - yz- zx is always positive

If x+y -z = 4 and x^(2) + y^(2) + z^(2) = 30 , then find the value of xy- yz- zx

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

If x!=y!=z and |x x^2 1+x^3 y y^2 1+y^3 z z^2 1+z^3|=0 , then prove that x y z=-1 .

If x+y+z=0,x^2+y^2+z^2=60, find xy + yz + zx

If the real numbers x, y, z are such that x^2 + 4y^2 + 16z^2 = 48 and xy + 4yz + 2zx = 24 . what is the value of x^(2) +y^(2) z^(2) =?

Factorise : (vi) x^(2) - y^(2) - 2yz - z^(2)

Multiply -5xy^(2), -3x^(2)yz and 8yz^(2) . Verify the result for x = 1, y = 2 and z = 3.

If x,y,z gt 0 and x + y + z = 1, the prove that (2x)/(1 - x) + (2y)/(1 - y) + (2z)/(1 - z) ge 3 .