Question

Prove that x³ + y³ = z³

Answer 1

x³ + y³ + z³ - 3xyz

= ( x + y + z ) ( x² + y² + z² - xy - yz - zx )

Multiply and divided by 2

= 1/2 ( x + y + z ) ( 2x² + 2y² + 2 z² - 2xy - 2yz - 2zx )

= 1/2 (x+y+z) ( x² - 3xy + y² + y² - 2 yz + z² + z² - 2zx + x² )

= 1/2 ( x+ y + z) { ( x - y )² + ( y - z ) ² + ( z - x )² }