what is the proof of x + y + z = 3xyz?

Question

what is the proof of x + y + z = 3xyz if x + y + z = 0

Sorry i didn't realize this but the actual formula is

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

Answer 1

It doesn't.

Answer 2

This is not a right statement!

if x = -1=y, z = 2 then x+y+z=0 but 3xyz = 6 not 0!!!

Answer 3

There is no proof for this. They aren't like terms and cannot therefore be added as such. x+y+z=x+y+z, not 3xyz.

Answer 4

is it true ?

x = 1, y = 1, z =-2

then x+y+z = 0 but 3xyz is not 0

so your statement is not true.

Answer 5

ummm dude i checked that on google and x plus y plus z doesn't even equal to 3xyz!

Answer 6

do one element, i'm no longer proving it purely providing you with a touch. greater effective resolve that way extremely than assuming x, y and z with any random extensive form. you will desire to be understanding the formulation of (x+y+z)^3= x^3+y^3+z^3 + greater words. Now replace the lcm of your expression with (x+y+z)^3 - greater words. desire you get some concept appropriate to the question

Answer 7

The above is not true

the correct statement is

if x+y+z = 0

then x^3+y^3+z^3 = 3xyz

to prove it

x+y = -z
cube both sides

(x+y)^3 = - z^3
or x^3+y^3+3xy(x+y) = - z^3
or x^3+y^3+z^3 = -3xy(x+y)
= -3xy(-z) as x+y = -z
= 3xyz
proved

=

Answer 8

PROOF IS THIS :

X=0,Y=0,Z=0

THEREFORE ONLY THAN, X+Y+Z = 0+0+0 = 0

WHICH EQUALS 3 x X x Y x Z = 3*0*0*0 = 0


L.H.S = R.H.S

HENCE PROVED


HUH! SO SIMPLE THING

Answer 9

lhs=rhs, right? lets see.....uh.....

let x,y,and z = 0.
0+0+0=3(0)(0)(0)
0=0

i'm really not sure if im right becauz i'm only in 8th grade, technically 7th cuz i skipped one.

Answer 10

x = y = z = 1

therefore

x + y + z = 3

and 3*x*y*z = 3

so x + y + z = 3*xyz (multiplicative property of monotonic binary addition)

That was too fun... oh us engineers find pleasure in the simplest of things

Answer 11

impossible, unless you assume some numbers for X,Y and Z