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Step-by-step explanation:
a + b + c = 6
= a + b + c - 2 - 2 - 2 = 0
= 2 - a + 2 - b + 2 - c = 0
We know that if x + y + z = 0 , x³ + y³ + z³ = 3 xyz .
This means that the given equation in the question will be equal to :
( 2 - a )³ + ( 2 - b )³ + ( 2 - c )³ = 3 ( 2 - a )( 2 - b )( 2 - c ) .
Transpose the right hand side values to the left :
⇒ ( 2 - a )³ + ( 2 - b )³ + ( 2 - c )³ - 3 ( 2 - a )( 2 - b )( 2 - c ) = 0
Hence the value will be 0 .
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