If a+b+c =2, ab+bc+ca= -1 and abc =-2 find the value of a cube + b cube + c cube.
Answers
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]
_____________________________
the answer is 8
Step-by-step explanation:
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