Question

If x+y+z=0, then prove that x^3+y^3+z^3=3xyz.​

Answer 1

Step-by-step explanation:

proved xplus y plus z is 0 then x cube y cube and z cube is equal to 3xyz

Answer 2

Solution:-

It Is Given that,

x + y + z = 0.

To Prove,

x³ + y³ + z³ = 3xyz.

Proof,

We know that,

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

Now, We Can Put the value Of (x + y + z).

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

➭x³ + y³ + z³ - 3xyz = 0.

➭x³ + y³ + z³ = 3xyz.

Hence, Proved.