Question : If $x\left(3-\frac{2}{x}\right)=\frac{3}{x}$, then the value of $x^3-\frac{1}{x^3}$ is equal to:
Option 1: $\frac{8}{27}$
Option 2: $\frac{61}{27}$
Option 3: $\frac{62}{27}$
Option 4: $\frac{52}{27}$
Latest: SSC CGL Tier 1 Result 2024 Out | SSC CGL preparation tips to crack the exam
Don't Miss: SSC CGL Tier 1 Scorecard 2024 Released | SSC CGL complete guide
Suggested: Month-wise Current Affairs | Upcoming Government Exams
Correct Answer: $\frac{62}{27}$
Solution : $x\left(3-\frac{2}{x}\right)=\frac{3}{x}$ ⇒ $3x-2 = \frac{3}{x}$ ⇒ $3x- \frac{3}{x} = 2$ ⇒ $(x- \frac{1}{x}) = \frac{2}{3}$ $\because$ $(x-y)^3 = x^3-y^3-3xy(x-y)$ $(x- \frac{1}{x})^3 = (\frac{2}{3})^3$ ⇒ $x^3-\frac{1}{x^3} - 3(x-\frac{1}{x}) = \frac{8}{27}$ ⇒ $x^3-\frac{1}{x^3} - 3(\frac{2}{3}) = \frac{8}{27}$ ⇒ $x^3-\frac{1}{x^3} = \frac{8}{27}+2$ ⇒ $x^3-\frac{1}{x^3} = \frac{62}{27}$ Hence, the correct answer is $\frac{62}{27}$.
Candidates can download this ebook to know all about SSC CGL.
Result | Eligibility | Application | Selection Process | Preparation Tips | Admit Card | Answer Key
Question : If $x^{2} -3x +1=0$, then the value of $\frac{\left(x^4+\frac{1}{x^2}\right)}{\left(x^2+5 x+1\right)}$ is:
Question : If $\frac{x}{2}-\frac{\left [4\left (\frac{15}{2}-\frac{x}{3} \right ) \right ]}{3} = –\frac{x}{18}$ then what is the value of $x$?
Question : If $\frac{1}{x^2+a^2}=x^2-a^2$, then the value of $x$ is:
Question : If $2x+\frac{1}{2x}=2,$ what is the value of $\sqrt{2\left (\frac{1}{x}\right)^{4}+\left (\frac{1}{x}\right)^{5}}\; ?$
Question : If $\left(x-\frac{1}{x}\right)^2=12$, what is the value of $\left(x^2-\frac{1}{x^2}\right)$, given that $x>0$?
Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile