Question

If 3x + y + z = 0, show that 27 x³+y³+ z³ = 9xyz

Answer 1

Hey



Given that :-


3x + y + z = 0


To prove :-

27x³ + y³ + z³ = 9xyz .


Proof :-


We know that ,


if ( a + b + c ) = 0

then ,

( a³ + b³ + c³ ) 3abc .


Same formulae will be applied here ,


3x + y + z = 0


then


( 3x ) ³ + ( y ) ³ + ( z ) ³ = 3 * 3x * y * z


=> 27x³ + y³ + z³ = 9xyz



thanks :)