Question

If x+y+z =0 Show that x3+y3+z3=3xyz​

Answer 1

x + y + z = 0

x + y = -z ... (i)

cubing both the sides

(x + y)³ = (-z)³

x³ + y³ + 3xy(x + y) = -z³

x³ + y³ + 3xy(-z) = -z³ ... (from (i))

x³ + y³ - 3xyz = -z³

x³ + y³ + z³ = 3xyz

... Hence Proved!