Question

X cube + Y cube + Z cube + kxyz is divisible by X + Y + Z the value of k

Answer 1

the value of k is -3

Answer 2

Answer will be (-3)

${a}^{3} + {b}^{3} + {c}^{3} - 3abc$
is equal to
(a+b+c)(a^2+b^2+c^2-ab-bc-ca)

This is divisible by (a+b+c)

so, x^3 + y^3 + z^3 + kxyz is of the form
a^3 +b^3+c^3 - 3abc

Hence,
k is -3


Hope you get it ...