SSC CHSL 12 Aug 2021 Shift 3 Paper

Section: Quantitative Aptitude

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Question : 67 of 99

Marks: +1, -0

If

x+\;{1}/{x}=√{13}

, then one of the values of

x^{3}-\;{1}/{x^{3}}

is

$4 √{11}$
32
$4 √{13}$
36

Solution:

Given,

x+\;{1}/{x}=√{13}

∴ (x-\;{1}/{x})^{2} \;\; =(x+\;{1}/{x})^{2}-4

\;\; =(√{13})^{2}-4=13-4=9

⇒(x-\;{1}/{x})=√{9}=3

We know that,

x^{3}-\;{1}/{x^{3}}= \;\; (x-\;{1}/{x})^{3}

+3 × x × \;{1}/{x} ×(x-\;{1}/{x})

∴ \;\; x^{3}-\;{1}/{x^{3}}= \;\; (3)^{3}+3 ×(3)

= \;\; 27+9=36

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