Question

If x+y+z=0show that x² + y³+z³=3×yz

Answer 1

We know that ,

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

Given that :- x + y + z = 0

x³ + y³ + z³ - 3xyz = 0 ( x² + y² + z² - xy - yz - zx )

Any number multipled by 0 is 0 .

So , x³ + y³ + z³ - 3xyz = 0

x³ + y³ + z³ = 3xyz

Hence proved