x−1x=2,x−1x=2,x - \frac{1}{x} = 2{\text{,}} then the value of the following is x3−1x3" role="presentation">x3−1x3x3−1x3{x^3} - \frac{1}{{{x^3}}} = ?" /> x−1x=2,x−1x=2,x - \frac{1}{x} = 2{\text{,}} then the value of the following is x3−1x3" role="presentation">x3−1x3x3−1x3{x^3} - \frac{1}{{{x^3}}} = ?" /> x−1x=2,x−1x=2,x - \frac{1}{x} = 2{\text{,}} then the value of the following is x3−1x3" role="presentation">x3−1x3x3−1x3{x^3} - \frac{1}{{{x^3}}} = ?" />

India’s No.1 Educational Platform For UPSC,PSC And All Competitive Exam

Download Our App

If $x - \frac{1}{x} = 2,$ $x - \frac{1}{x} = 2{\text{,}}$ then the value of the following is $x^{3} - \frac{1}{x^{3}}$ ${x^3} - \frac{1}{{{x^3}}}$ = ?

12
211
315
414

Answer:- 1

Explanation:-

Solution:

\begin{aligned} x - \frac{1}{x} = 2 to find x^{3} - \frac{1}{x^{3}} \\ \Rightarrow x - \frac{1}{x} = 2 \\ [Cubing both sides] \\ \Rightarrow {(x - \frac{1}{x})}^{3} = {(2)}^{3} \\ \Rightarrow x^{3} - \frac{1}{x^{3}} - 3 \times x \times \frac{1}{x} (x - \frac{1}{x}) = 8 \\ \Rightarrow x^{3} - \frac{1}{x^{3}} - 3 \times (2) = 8 \\ \Rightarrow x^{3} - \frac{1}{x^{3}} = 14 \end{aligned}

$\eqalign{ & x - \frac{1}{x} = 2{\text{ to find }}{x^3} - \frac{1}{{{x^3}}} \cr & \Rightarrow x - \frac{1}{x} = 2 \cr & \left[ {{\text{Cubing both sides}}} \right] \cr & \Rightarrow {\left( {x - \frac{1}{x}} \right)^3} = {\left( 2 \right)^3} \cr & \Rightarrow {x^3} - \frac{1}{{{x^3}}} - 3 \times x \times \frac{1}{x}\left( {x - \frac{1}{x}} \right) = 8 \cr & \Rightarrow {x^3} - \frac{1}{{{x^3}}} - 3 \times \left( 2 \right) = 8 \cr & \Rightarrow {x^3} - \frac{1}{{{x^3}}} = 14 \cr}$

Workspace Report

Post your Comments

then the value of the following is

x^{3} - \frac{1}{x^{3}}

${x^3} - \frac{1}{{{x^3}}}$ = ?", "text": "If

x - \frac{1}{x} = 2,

$x - \frac{1}{x} = 2{\text{,}}$ then the value of the following is

x^{3} - \frac{1}{x^{3}}

${x^3} - \frac{1}{{{x^3}}}$ = ?", "dateCreated": "7/24/2019 10:09:12 AM", "author": { "@type": "Person", "name": "Nitin Sir" }, "answerCount": "4", "acceptedAnswer": { "@type": "Answer", "text": "

Solution:

\begin{aligned} x - \frac{1}{x} = 2 to find x^{3} - \frac{1}{x^{3}} \\ \Rightarrow x - \frac{1}{x} = 2 \\ [Cubing both sides] \\ \Rightarrow {(x - \frac{1}{x})}^{3} = {(2)}^{3} \\ \Rightarrow x^{3} - \frac{1}{x^{3}} - 3 \times x \times \frac{1}{x} (x - \frac{1}{x}) = 8 \\ \Rightarrow x^{3} - \frac{1}{x^{3}} - 3 \times (2) = 8 \\ \Rightarrow x^{3} - \frac{1}{x^{3}} = 14 \end{aligned}

$\eqalign{ & x - \frac{1}{x} = 2{\text{ to find }}{x^3} - \frac{1}{{{x^3}}} \cr & \Rightarrow x - \frac{1}{x} = 2 \cr & \left[ {{\text{Cubing both sides}}} \right] \cr & \Rightarrow {\left( {x - \frac{1}{x}} \right)^3} = {\left( 2 \right)^3} \cr & \Rightarrow {x^3} - \frac{1}{{{x^3}}} - 3 \times x \times \frac{1}{x}\left( {x - \frac{1}{x}} \right) = 8 \cr & \Rightarrow {x^3} - \frac{1}{{{x^3}}} - 3 \times \left( 2 \right) = 8 \cr & \Rightarrow {x^3} - \frac{1}{{{x^3}}} = 14 \cr}$ ", "dateCreated": "7/24/2019 10:09:12 AM", "author": { "@type": "Person", "name": "Nitin Sir" } }, "suggestedAnswer": { "@type": "Answer", "text": "

Solution:

\begin{aligned} x - \frac{1}{x} = 2 to find x^{3} - \frac{1}{x^{3}} \\ \Rightarrow x - \frac{1}{x} = 2 \\ [Cubing both sides] \\ \Rightarrow {(x - \frac{1}{x})}^{3} = {(2)}^{3} \\ \Rightarrow x^{3} - \frac{1}{x^{3}} - 3 \times x \times \frac{1}{x} (x - \frac{1}{x}) = 8 \\ \Rightarrow x^{3} - \frac{1}{x^{3}} - 3 \times (2) = 8 \\ \Rightarrow x^{3} - \frac{1}{x^{3}} = 14 \end{aligned}

$\eqalign{ & x - \frac{1}{x} = 2{\text{ to find }}{x^3} - \frac{1}{{{x^3}}} \cr & \Rightarrow x - \frac{1}{x} = 2 \cr & \left[ {{\text{Cubing both sides}}} \right] \cr & \Rightarrow {\left( {x - \frac{1}{x}} \right)^3} = {\left( 2 \right)^3} \cr & \Rightarrow {x^3} - \frac{1}{{{x^3}}} - 3 \times x \times \frac{1}{x}\left( {x - \frac{1}{x}} \right) = 8 \cr & \Rightarrow {x^3} - \frac{1}{{{x^3}}} - 3 \times \left( 2 \right) = 8 \cr & \Rightarrow {x^3} - \frac{1}{{{x^3}}} = 14 \cr}$ ", "dateCreated": "7/24/2019 10:09:12 AM" } }

Test

Classes

E-Book