Question

If x+y+z=0 show that
x+y+zº = 3xyz​

Answer 1

I think the question is if x+y+z=0then show xcube +ycube+ zcube= 3xyz

then the answer is

If X+y+z =0

We know that: a cube + B cube + c cube -3abc = (a+B+c) ( a ^2 + b^2 + c^2 -ab-bc-ca)

Now if we put the value of X+y+z that is 0, we will get:

= (0) ( X sq + y sq + z sq- xy- yz-zx)

If we multiply anything by zero,the answer is 0

Therefore,

X cube + y cube+ zcube- 3 X y z = 0

Therefore

X cube + y cube + z cube = 3 X y z