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SSC CHSL 2023 PYQ — Question 54

SSC CHSL - 09 Aug 2023 - Shift 4 • Quantitative Aptitude • Q54

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If x = (7 + 353\sqrt5), then fine the value of x2 + 1x2\frac{1}{x^2}

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Correct answer: D

Explanation

The correct answer is Option 4 i.e. 799+315​​58\frac{799+315​​\sqrt5}{8}.

x=7+35x=7 + 3\sqrt5

⇒ 1x=17+35=(7−35)(7+35)(7−35)=7−354\frac{1}{x}=\frac{1}{7+3\sqrt5}= \frac{(7-3\sqrt5)}{(7+3\sqrt5)(7-3\sqrt5)}=\frac{7-3\sqrt5}{4}

⇒ x+1x=(7+35)+(7−35)4=35+954x+\frac{1}{x}=(7+3\sqrt5)+\frac{(7-3\sqrt5)}{4}=\frac{35+9\sqrt5}{4}

⇒ x2+1x2=(35+954)2−2x^2+\frac{1}{x^2}=\left(\frac{35+9\sqrt5}{4} \right)^2-2

=1630+630516−2=\frac{1630+630\sqrt5}{16}-2

=799+315​​58=\frac{799+315​​\sqrt5}{8}