Question

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

Answer 1

Answer:

hope it helps you

Step-by-step explanation:

Acc to identity -

X3 + y3 + c3 - 3xyz = ( x+y+z )(x2 + y2 + z2 - xy - yz - zx )

here x + y + z = 0

therefore, X3 + y 3 + z3 - 3 xyz = 0 * ( x2 + y2 + z2 - xy - yz - zx )

X3 + y3 + z3 - 3 xyz = 0

X3 + y3 + z3 = 3xyz

Answer 2

x + y + z = 0

» x³ + y³ + z³ - 3xyz

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

But, x + y + z = 0

» x³ + y³ + z³ - 3xyz

= (0) (x² + y² + z² - xy - yz - zx)

» x³ + y³ + z³ - 3xyz = 0

Therefore, x³ + y³ + z³ = 3xyz