Verify that `x^3 + y^3 + z^3- 3xyz=1/2 (x+y+z)[(x-y)^2+(y-z)^2+(z-x)^2]`

If x+y+z=0, show that x^3 + y^3+z^3- 3xyz .

If u = log (x^(3) + y^(3) + z^(3) - 3xyz) , then (x + y + z)(u_(x) + u_(y) + u_(z)) is equal to

11x y^2 z^3 // 55xyz = ___

If x+y+z=0 show that x^(3)+y^(3)+z^(3)=3xyz .

If Tan^(-1)x+Tan^(-1)y+Tan^(-1)z=(pi)/2 and (x-y)^(2)+(y-z)^(2)+(z-x)^(2)=0 then x^(2)+y^(2)+z^(2)=

In a triangle XYZ, let x,y,z be the lengths of sides opposite to the angles X, Y, Z, respectively, and 2s = x + y + z . " If" (s - x)/4 = (x - y)/3 = (x - z)/2 and area o incircle of the triangle XYZ is (8pi)/3 , then

The equations x+2y-z=3, 3x-y+2z=1, 2x-2y+3z=2 have

For the equations x+2y+3z=1, 2x+y+3z=2, 5x+5y+9z=4