Question : If $x^{2} + \frac{1}{x^{2}} = 18$ and $x > 0$, what is the value of $x^{3} + \frac{1}{x^{3}}?$
Option 1: $36 \sqrt{5}$
Option 2: $40 \sqrt{5}$
Option 3: $46 \sqrt{5}$
Option 4: $34 \sqrt{5}$
Latest: SSC CGL preparation tips to crack the exam
Don't Miss: SSC CGL complete guide
New: Unlock 10% OFF on PTE Academic. Use Code: 'C360SPL10'
Correct Answer: $34 \sqrt{5}$
Solution : $x^{2} + \frac{1}{x^{2}} = 18$ ⇒ $x^{2} + \frac{1}{x^{2}} + 2 = 18+2$ ⇒ $(x + \frac{1}{x})^{2} = 20$ ⇒ $(x + \frac{1}{x}) = \sqrt{20}$ Now, $(x + \frac{1}{x})^{3}=x^3+\frac{1}{x^3}+3 × x × \frac{1}{x} × (x + \frac{1}{x})$ ⇒ $(\sqrt{20})^3=x^3+\frac{1}{x^3}+3×\sqrt{20}$ ⇒ $x^3+\frac{1}{x^3}=20\sqrt{20} - 3\sqrt{20}$ ⇒ $x^3+\frac{1}{x^3}=17\sqrt{20}$ $\therefore x^3+\frac{1}{x^3}=34\sqrt{5}$ Hence, the correct answer is $34\sqrt{5}$.
Candidates can download this ebook to know all about SSC CGL.
Answer Key | Eligibility | Application | Selection Process | Preparation Tips | Result | Admit Card
Question : If $x>0$ and $x^4+\frac{1}{x^4}=254$, what is the value of $x^5+\frac{1}{x^5}?$
Question : If $\left(x^2 - \frac{1}{x^2}\right) = 4 \sqrt{6}$ and $x>1$, what is the value of $\left(x^3 - \frac{1}{x^3}\right)?$
Question : If $(x+\frac{1}{x})=6$ and $x>1$, find the value of $(x^2–\frac{1}{x^2})$.
Question : If $\left(x^2+\frac{1}{x^2}\right)=7$, and $0<x<1$, find the value of $x^2-\frac{1}{x^2}$.
Question : If $\frac{\sqrt{5+x}+\sqrt{5-x}}{\sqrt{5+x}-\sqrt{5-x}}=3$, what is the value of $x$?
Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile