Math, asked by mrrajeshsonypcbpz9, 1 year ago

If x+y +z=0 then prove that x 3 +y 3 +z 3 =3xyz


Answers

Answered by nikolatesla2
6
Given, x3 + y3 + z3 = 3xyz

Therefore, x3 + y3 + z3 - 3xyz =0

This means,
x3 + y3 + z3 - 3xyz = (x + y + z) (x2 + y2 + z2 - xy - yz - zx)

Now if x + y + z = 0, then......

x3 + y3 + z3 - 3xyz = ( 0 ) (x2 + y2 + z2 - xy - yz - zx)  . . . . . . .... ..... ... .. . . .. . .....    [ subsituting the value of x + y + z ]

x3 + y3 + z3 - 3xyz = 0   

x3 + y3 + z3 = 3xyz .  

Answered by Arshad2003
2

Given, x3 + y3 + z3 = 3xyz


Therefore, x3 + y3 + z3 - 3xyz =0


This means,

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


Now if x + y + z = 0, then......


x3 + y3 + z3 - 3xyz = ( 0 ) (x2 + y2 + z2 - xy - yz - zx)  . . . . . . .... ..... ... .. . . .. . .....    [ subsituting the value of x + y + z ]


x3 + y3 + z3 - 3xyz = 0   


x3 + y3 + z3 = 3xyz .  

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