Question

ifx+y+z=0 show that x3+y3+z3=3xyz

Answer 1

Hey there!!

AIM : If x + y + z = 0 , then prove x³ + y³ + z³ = 3xyz

In order to prove this,

Let us use the formula :

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

Now, let us keep x + y + z = 0

x³ + y³ + z³ - 3xyz = 0

x³ + y³ + z³ = 3xyz

∴ Hence proved

#Together_we_Go_Far

Answer 2

(a+b+c)3=(a3+b3+c3)+3[(a+b+c)(ab+ac+bc)−abc]
since x+y+x=0
$x 3 + y3 + z3 = 3xyz$