Question : If $\left(y+\frac{1}{y}\right)=4$, then find the value of $\left(y^6+\frac{1}{y^6}\right)$.
Option 1: 2702
Option 2: 2704
Option 3: 4096
Option 4: 2706
Correct Answer: 2702
Solution :
Given:
$\left(y+\frac{1}{y}\right)=4$
Squaring both sides, we get
⇒ $\left(y+\frac{1}{y}\right)^{2}=4^{2}$
⇒ $y^{2}+\frac{1}{y^{2}}=16-2$
⇒ $y^{2}+\frac{1}{y^{2}}=14$
Cubing both sides, we get
⇒ $(y^{2}+\frac{1}{y^{2}})^3=14^3$
⇒ $\left(y^6+\frac{1}{y^6}\right)+3×\left(y^2×\frac{1}{y^2}\right)×\left(y^2+\frac{1}{y^2}\right)=2744$
⇒ $\left(y^6+\frac{1}{y^6}\right)+3×14=2744$
⇒ $\left(y^6+\frac{1}{y^6}\right)=2744-42$
$\therefore \left(y^6+\frac{1}{y^6}\right)=2702$
Hence, the correct answer is 2702.
Related Questions
Know More about
Staff Selection Commission Combined Grad ...
Admit Card | Eligibility | Application | Selection Process | Preparation Tips | Result | Answer Key
Get Updates Brochure
Your Staff Selection Commission Combined Graduate Level Exam brochure has been successfully mailed to your registered email id “”.
