Question

x+y+z=0, show that x*3+y*3+z*3=3xyz

Answer 1

Taking all whole numbers:
x+y+z=0
0+0+0=0

x*3+y*3+z*3=3zyx
0*3+0*3+0*3=3*0*0*0
0+0+0=0
0=0

Hence proved.

Answer 2

Hey there!

Here we're Given, x+y+z = 0

As we all know that, (IDENTITY)

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

Now if x + y + z = 0, Then..

x³ + y³ + z³ - 3xyz = ( 0 ) (x² + y² + z² - xy - yz - zx)     
( Subsituting the value of x+y+z = 0, from Given )

x³ + y³ + z³ - 3xyz = 0   

x³ + y³ + z³ = 3xyz

HOPE IT HELPED ^_^
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