Question

if a + b + 2 is equal to zero then a cube + b cube + 8 is equal to

Answer 1

Given,

a + 2b + c = 0

⇒ a + 2b + c = 0

⇒ a + 2b = - c

Cubing on both sides :

⇒ ( a + 2b )^3 = ( - c )^3

⇒ a^3 + ( 2b )^3 + 3( a + 2b )( a x 2b ) = - c^3

⇒ a^3 + 8b^3 + 3( - c )( 2ab ) = - c^3 { a + 2b = - c }

⇒ a^3 + 8b^3 - 6abc = - c^3

⇒ a^3 + 8b^3 + c^3 = 6abc

Hence proved.