Question

If x+y+z=0,show that xcube+ycube+zcube=3xyz . Friends its urgent plz help me because tomorrow is my online test on maths .​

Answer 1

Answer:

Step-by-step explanation:

X+Y+Z=0 (GIVEN)

to show that =xcube+ycube+zcube=3xyz

=> taking x as 5 , y as (-5) and z as 0

=>ATQ

   x+y+z=0

=> 5+(-5)+0=5-5+0

=>0

hence , we have shown that x+y+z =0

now,

5cube + (-5)cube +0cube = 3xyz

125+(-125) + 0= 3*5*(-5)*0

125-125+0=15*0

0=0

LHS=RHS

Hence , shown that x cube +y cube +z cube=3xyz

HOPE IT HELPS U .....

Answer 2

Hello friend

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= 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