Verify:x^3+y^3=z^3-3xyz=1/2(x+y+z)

x³ + y³ + z³ – 3xyz = (x + y + z) (x² + y² + z² – xy – yz – xz)

x³ + y³ + z³ – 3xyz = 1/2* (x + y + z) 2 (x² + y² + z² – xy – yz – xz)

= 1/2(x + y + z) (2x² + 2y² + 2z² – 2xy – 2yz – 2xz)

= 1/2(x + y + z) [(x² + y² – 2xy) + (y² + z² – 2yz) + (x² + z² – 2xz)]

= 1/2(x + y + z) [(x - y)² + (y – z)² + (z – x)²]