If `a^x=b^y=c^z` and `abc=1` then find the value of `xy+yz+zx`

If a^x=b^y=c^z" and "abc=1 , then prove that xy+yz+zx=0 .

If x= b+c, y=c+a, z=a+b , then find the value of (x^2 + y^2 + z^2 -yz - zx-xy)/( a^(2) + b^(2) + c^(2) - bc - ca - ab)

If xy = a, xz = b, yz = c and abc ne 0 , find the value of x^2 + y^2 + z^2 in terms of a, b, c.

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

If x^2+y^2+z^2= xy+yz+zx then find the value of (x+y):z.

If matrix A=[02 y z x y-zx-yz] satisfies AT = A-1, then find the value of x, y, z.

If a^(x) =b^(y) =c^(z) and abc =1 then xy+yz+zx is equal to which of the following?