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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