\(\rm x = \frac{{\sqrt 5 - 2}}{{\sqrt 5 + 2}}\) అయితే, x² + x^-2 విలువ:

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Question

This question was previously asked in

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

Answer 1

ఇచ్చినది:

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

ఉపయోగించిన భావన:

x + 1/x = a అయితే, x² + 1/x² = a² - 2

గణన:

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

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

⇒ 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

∴ 4వ ఎంపిక సరైన సమాధానం.

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