Question

if X + Y + Z is equal to zero then what is the value of the x cube + y cube + Z cube

Answer 1

Hi ,

We know the identity ,

x^3 + y^3 + z^3

= ( x + y + z ) ( x^2 + y^2 + z^2 -xy -yz - xz ) + 3xyz --( 1 )

According to the given problem ,

x + y + z = 0 put this value in equation ( 1 )

x^3 + y^3 + z^3

= 0 ×( x^2 + y^2 + z^2 - xy - yz - zx ) + 3xyz

x^3 + y^3 + z^3 = 3xyz

I hope this helps you.


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Answer 2

if x+y+z =0 , then
x^3+y^3 +z^3 = 3xyz