Question : If a + b + c = 1, ab + bc + ca = –1, and abc = –1, then what is the value of a3 + b3 + c3?
Option 1: 1
Option 2: 5
Option 3: 3
Option 4: 2
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Correct Answer: 1
Solution : a 3 + b 3 + c 3 = (a + b + c)(a 2 + b 2 + c 2 – ab – bc – ac) + 3abc = (a + b + c)((a + b + c) 2 – 3ab – 3bc – 3ac) + 3abc = (1){1 2 –3(–1)} + 3(–1) = 1 Hence, the correct answer is 1.
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