On putting x = -1

Correct Option: C

On putting x = -1

Using Rule 21,
∴ a³ + b³ + c³ – 3abc = (a + b + c)(a² + b² + c² – ab – bc – ca)
If a + b + c = 0, then a³ + b³ + c³ = 3abc

Correct Option: D

Using Rule 21,
∴ a³ + b³ + c³ – 3abc = (a + b + c)(a² + b² + c² – ab – bc – ca)
If a + b + c = 0, then a³ + b³ + c³ = 3abc

Using Rule 21,
∴ a³ + b³ + c³ – 3abc = (a + b + c)(a² + b² + c² – ab – bc – ca)
If a + b + c = 0, then a³ + b³ + c³ = 3abc

Correct Option: D

Using Rule 21,
∴ a³ + b³ + c³ – 3abc = (a + b + c)(a² + b² + c² – ab – bc – ca)
If a + b + c = 0, then a³ + b³ + c³ = 3abc

Using Rule 21,
If a + b + c = 0, then a³ + b³ + c³ = 3abc
∴ When a – b – c = 0,
a³ - b³ - c³ = 3abc
i.e. a³ - b³ - c³ - 3abc = 0
Here,a = 4.965, b = 2.343, c = 2.6222
∴ a – b – c = 4.965 – 2.343 – 2.622 = 0
Hence, a³ - b³ - c³ - 3abc = 0

Correct Option: C

Using Rule 21,
If a + b + c = 0, then a³ + b³ + c³ = 3abc
∴ When a – b – c = 0,
a³ - b³ - c³ = 3abc
i.e. a³ - b³ - c³ - 3abc = 0
Here,a = 4.965, b = 2.343, c = 2.6222
∴ a – b – c = 4.965 – 2.343 – 2.622 = 0
Hence, a³ - b³ - c³ - 3abc = 0

Using Rule 21,
Here, a + b + c = 1.21 + 2.12 – 3.33 = 0
a³ - b³ - c³ - 3abc = 0 ( ∴ a + b + c = 0)

Correct Option: A

Using Rule 21,
Here, a + b + c = 1.21 + 2.12 – 3.33 = 0
a³ - b³ - c³ - 3abc = 0 ( ∴ a + b + c = 0)