If x^{2}+\frac{1}{x^{2}}=83, x > 0, then the value of x^{3}-\frac{1}{x^{3}} is

SSC CHSL 12 Aug 2021 Shift 3 Paper

Section: Quantitative Aptitude

Question : 63 of 99

Marks: +1, -0

x^{2}+\;{1}/{x^{2}}=83, x > 0

, then the value of

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

Solution:

Given,

x^{2}+\;{1}/{x^{2}}=83

⇒ x^{2}+\;{1}/{x^{2}}-2+2=83

⇒\;(x-\;{1}/{x})^{2}+2 \;\; =83

⇒\;(x-\;{1}/{x})^{2} \;\; =83-2=81

⇒\;x-\;{1}/{x} \;\; =√{81}=9

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

\;+3\;× x × \;{1}/{x} ×(x-\;{1}/{x})

\;\; =(9)^{3}+3 × 9

\;\; =729+27=756

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