Question

QUESTION 13
CLASS 9 MATHS

ANSWER CORRECTLY
WHOEVER WILL ANSWER CORRECTLY WILL BE MARKED AS A BRAINLIEST ❤️

If x+y+z = 0, show that x3+y3+z3 = 3xyz.

Answer 1

$x+y+z = 0 \\ => x + y = -z \:\:\:\:\: (i) \\ => \bf{Cubing\: Both\:Sides} \\ => (x+y)³ = (-z)³ \\ => \bf \color{purple}{(a+b)³ = a³ + b³ + 3ab(a+b)} \\ =>x³ + y³ + 3xy(x+y) = -z³ \\ => x³ + y³ + 3xy(-z) = -z³ \:\:\:\:\:(from\:equation\:i) \\ => x³ + y³ -3xyz = -z³ \\ => \boxed{x³ + y³ + z³ = 3xyz}$

Hence Proved