If \(\rm x = \frac{{\sqrt 5 - 2}}{{\sqrt 5 + 2}}\), then the value of x² + x^-2 is:

Question

Question

This question was previously asked in

SSC CGL 2022 Tier-I Official Paper (Held On : 02 Dec 2022 Shift 1)

Answer 1

Given:

\(\rm x = \frac{{\sqrt 5 - 2}}{{\sqrt 5 + 2}}\)

Concept Used:

If x + 1/x = a, then x² + 1/x² = a² - 2

Calculation:

⇒ \(\rm x = \frac{{\sqrt 5 - 2}}{{\sqrt 5 + 2}}\)

⇒ \(\rm \frac{1}{x} = \frac{{\sqrt 5 + 2}}{{\sqrt 5 - 2}}\)

⇒ x + 1/x = \(\frac{{\sqrt 5 - 2}}{{\sqrt 5 + 2}} + \frac{{\sqrt 5 + 2}}{{\sqrt 5 - 2}}\)

⇒ x + 1/x = \(\frac{(\sqrt 5 - 2)^2 + (\sqrt 5 + 2)^2}{(\sqrt 5 +2)(\sqrt 5 - 2)}\)

⇒ x + 1/x = 18

⇒ x2 + 1/x2 = a2 - 2

⇒ x2 + 1/x² = 18² - 2

⇒ 322

∴ Option 4 is the correct answer.

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