If a - 2b + 3c = 0; state the value of a 3 - 8b 3 + 27c 3 .

By property, If x + y + z = 0, then : x 3 + y 3 + z 3 = 3xyz. Given, ⇒ a - 2b + 3c = 0 ⇒ a + (-2b) + 3c = 0 ∴ a 3 + (-2b) 3 + (3c) 3 = 3 × a × (-2b) × 3c ⇒ a 3 - 8b 3 + 27c 3 = -18abc. Hence, a 3 - 8b 3 + 27c 3 = -18abc.

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Mathematics

If a - 2b + 3c = 0; state the value of a³ - 8b³ + 27c³.

Expansions

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Answer

By property,

If x + y + z = 0, then :

x³ + y³ + z³ = 3xyz.

Given,

⇒ a - 2b + 3c = 0

⇒ a + (-2b) + 3c = 0

∴ a³ + (-2b)³ + (3c)³ = 3 × a × (-2b) × 3c

⇒ a³ - 8b³ + 27c³ = -18abc.

Hence, a³ - 8b³ + 27c³ = -18abc.

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Mathematics

If a - 2b + 3c = 0; state the value of a³ - 8b³ + 27c³.

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If a + b = 11 and a² + b² = 65; find a³ + b³.