Question

If a + b + c = 2, ab + bc + ca = −1 and abc = −2, find the value of a³ + b³ + c³.

Answer 1

a + b + c = 2

ab + bc + ca = - 1

abc = - 2

____________ [GIVEN]

• We have to find the value of a³ + b³ + c³

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a + b + c = 2                                                                                                         • Square on both sides

=> (a + b + c)² = (2)²

=> a² + b² + c² + 2ab + 2bc + 2ca = 4

=> a² + b² + c² + 2(ab + bc + ca) = 4

=> a² + b² + c² + 2(-1) = 4

=> a² + b² + c² - 2 = 4

=> a² + b² + c² = 4 + 2

=> a² + b² + c² = 6

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=> a³ + b³ + c³ - 3abc = (a + b + c) (a² + b² + c² - ab - bc - ca)

=> a³ + b³ + c³ - 3abc = (a + b + c) [a² + b² + c² - (ab + bc + ca)]

=> a³ + b³ + c³ - 3(-2) = (2) [6 - (-1)]

=> a³ + b³ + c³ + 6 = 2(6 + 1)

=> a³ + b³ + c³ + 6 = 2(7)

=> a³ + b³ + c³ + 6 = 14

=> a³ + b³ + c³ = 14 - 6

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a³ + b³ + c³ + 6 = 7

___________ [ANSWER]

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Answer 2

Explanation:

your answer is 1

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