Question

x+y+z=0,x³+y³+z³=3xyz​

Answer 1

Step-by-step explanation:

Hello friend

_________________________________________________________

= Put x + y + z = 0 ,

= x³ + y³ + z³ - 3xyz = ( 0 ) ( x² + y² + z² - xy - yz - zx )

= x³ + y³ + z³ - 3xyz = 0

= x³ + y³ + z³ = 3xyz

hope it helps u ☺

Answer 2

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GIVEN :-

x+y+z=0............( 1 )

TO FIND :-

Prove that x+y+z=0,x³+y³+z³=3xyz

SOLUTION :-

Then

x + y = - z

Cubing on Both Sides

( x + y )³ = z³

Formula = (x+y)³ = x³+3xy(x+y)+y³

So, Here also

x³ + 3xy( x + y )+y³ = - z³

x³ + 3xy( - z )+ y³ = - z³

HENCE,

x³ + y³ + z³ = 3xy