If x+\frac{1}{x}=7, then x^{3}+\frac{1}{x^{3}} is equal to

SSC CHSL 16 Apr 2021 Shift 2 Paper

Section: Quantitative Aptitude

Question : 58 of 100

Marks: +1, -0

x+\;{1}/{x}=7

, then

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

is equal to

Solution:

Given,

x+\;{1}/{x}=7

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

\;×(x+\;{1}/{x})

⇒ x^{3}+\;{1}/{x^{3}} \;\; =(7)^{3}-3 ×(7)

\;\; =343-21=322

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