If x + \(\frac{1}{x}\) = 1, then the value of x12 + x9 + x6 + x3 + 1 is:

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SSC CGL 2022 Tier-I Official Paper (Held On : 06 Dec 2022 Shift 1)
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  1. 1
  2. -1
  3. 0
  4. -2

Answer (Detailed Solution Below)

Option 1 : 1
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PYST 1:SSC CGL 2023 - Quantitative Aptitude(Held On:14 Jul 2023 Shift 1)
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Detailed Solution

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Given:

The value of x12 + x9 + x6 + x3 + 1

if x + (1/x) = 1

x2 + 1 = x

x2 - x + 1 = 0

(x + 1)(x2 - x + 1) = 0 (x + 1)

(x3 + 13) = 0

x3 = -1

Formula used:

x + 1/x = 1 then x3 = -1

Calculation:

According to the question,

x12 + x9 + x6 + x3 + 1

⇒ (x3)4 + (x3)3 + (x3)2 + (x3) + 1

⇒ (−1)4 + (-1)3 + (-1)2 + (-1) + 1 

⇒ 1 - 1 + 1  - 1 + 1

⇒ 3 - 2 = 1

∴ The value of x12 + x9 + x6 + x3 + 1 is 1.

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