if a + b + 3c = 0 then prove that a^3+8b^3+27c^3 = 18abc
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Step-by-step explanation:
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
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