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If $$x + \frac{1}{x} = 1,$$ then the value of x12 + x9 + x6 + x3 + 1 is:
Answer & Solution
Correct Answer:
Option
A
$$x + \frac{1}{x} = 1$$
x2 + 1 - x = 0
(x + 1)(x2 + 12 - x) = 0
x3 + 1 = 0
x3 = -1
⇒ x12 + x9 + x6 + x3 + 1
= 1 - 1 + 1 - 1 + 1
= 1
x2 + 1 - x = 0
(x + 1)(x2 + 12 - x) = 0
x3 + 1 = 0
x3 = -1
⇒ x12 + x9 + x6 + x3 + 1
= 1 - 1 + 1 - 1 + 1
= 1
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