Question

If x+y+z=0,show that x cube +y cube +z cube equal to 3xyz

Answer 1

Answer:

When we have formula i.e x cube plus y cube plus z cube minus 3xyz = .......

Step-by-step explanation:

RHS contains X+Y+Z multiplied by other stuff and since x+y+z is zero RHS become zero

Therefore minus 3 xyz goes right side and become positive ..

Hpe u Understand

Answer 2

Answer:

Step-by-step explanation:

Proof:

  x + y + z = 0

Therefore, x + y = -z                                      eqn 1.

Cubing on both the sides we get,

(  x + y )^3  =( -z)^3    

Therefore, we get,

x^3 + y^3 + 3x^2y + 3x^y = -z^3

Transposing RHS TO lhs,

X^3  + Y^3 + Z^3 = -3xy(x+y)

From eqn1,

x^3 + y^3 + z^3 = -3xy( -z)

Thus, x^3 + y^3 + z^3 = 3xyz

HOPE THIS HELPS YOU...