Question

if a+2b+3c=0 prove a3 +8b3+27c3=18abc

Answer 1

if a + 2b + 3c = 0 

then a3 + 8b3 + 27c3 = 18abc 

if a-2b-3c=0 then ........changing the signs 

a3 - 8b3 - 27c3 = 18abc

i hope it helps u

Answer 2

Hi ,

a + 2b + 3c = 0 ---( 1 )

a + 2b = - 3c ---( 2 )

( a + 2b )³ = ( - 3c )³

a³ + ( 2b )³ + 3 × a × 2b ( a + 2b ) = - 27c³

a³ + 8b³ + 27c³ + 6ab × ( - 3c ) = 0

[from ( 2 ) ]

a³ + 8b³ + 27c³ - 18abc = 0

a³ + 8b³ + 27c³ = 18abc

Hence proved .

I hope this helps you.

: )