The value of ( x - y )^3 + ( y - z )^3 + ( z - x )^3 ( x^2 - y^2 )^3…

Question

The value of ( x - y )^3 + ( y - z )^3 + ( z - x )^3 ( x^2 - y^2 )^3 + ( y^2 - z^2 )^3 + ( z^2 - x^2 )^3 is = ?

Accepted Answer

Option D. [ ( x + y ) ( y + z ) ( z + x ) ]^ - 1. Answer & Solution Answer: Option D Solution: & Since ( x - y ) + ( y - z ) + ( z - x ) = 0 & So, ( x - y )^3 + ( y - z )^3 + ( z - x )^3 & = 3 ( x - y ) ( y - z ) ( z - x ) & Since ( x^2 - y^2 ) + ( y^2 - z^2 ) + ( z^2 - x^2 ) = 0 & So, ( x^2 - y^2 ) + ( y^2 - z^2 ) + ( z^2 - x^…