Question

If X + Y + Z is equal to zero show that x cube + y cube + Z cube is equals to 3 x y z

Answer 1

Answer:

Step-by-step explanation:

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

Hence proved...

Answer 2

$\bold{Answer}$

If x + y + z = 0, show that x³ + y³ + z³ = 3xyz

Sol : x + y + z = 0

=> x + y = - z

cubing both sides, we get:

(x + y)³ = (-z)³

=> x³ + y³ + 3xy (x + y) = -z³

=> x³ + y³ + 3xy (-z) = -z³

[From (i) x + y = - z]

=> x³ + y³ - 3xyz = -z³

=> x³ + y³ + z³ = 3xyz

Hence Proved