Question

if X + Y + 2 equal to zero then find the value of x cube + y cube + 8

Answer 1

$\sf{x + y + 2 = 0}$

$\sf{or \: \: \: x + y = - 2}$

cubing on both sides.

$\sf{{(x + y)}^{3} = {- 2}^{3} }$

$\sf{ {x}^{3} + {y}^{3} + 3xy(x + y)= - 8}$

$\sf{ {x}^{3} + {y}^{3} + 3xy( - 2)= - 8}$

$\sf{ {x}^{3} + {y}^{3} - 6xy= - 8}$

$\fbox{ \sf{ {x}^{3} + {y}^{3} + 8= 6xy}}$