Question : If $p^2+\frac{1}{p^2}=14$, then find the value of $\left(p^3+\frac{1}{p^3}\right)$.
Option 1: 56
Option 2: 60
Option 3: 48
Option 4: 52
New: SSC CHSL Tier 2 answer key released | SSC CHSL 2024 Notification PDF
Recommended: How to crack SSC CHSL | SSC CHSL exam guide
Don't Miss: Month-wise Current Affairs | Upcoming government exams
Correct Answer: 52
Solution :
Given: $p^2+\frac{1}{p^2}=14$
we know that,
$p^2+\frac{1}{p^2}=(p+\frac{1}{p})^2-2\times p\times \frac{1}{p}$
$⇒(p+\frac{1}{p})^2-2\times p\times \frac{1}{p}=14$
$⇒(p+\frac{1}{p})^2=14+2$
$⇒(p+\frac{1}{p})^2=16$
$⇒(p+\frac{1}{p})=4$
Now cubing both sides, we get:
$⇒(p+\frac{1}{p})^3=4^3$
$⇒p^3+\frac{1}{p^3}+3\times p\times \frac{1}{p}(p+ \frac{1}{p})=4^3$
$⇒p^3+\frac{1}{p^3}+3\times4=64$
$⇒p^3+\frac{1}{p^3}=64-12$
$⇒p^3+\frac{1}{p^3}=52$
Hence, the correct answer is 52.
Related Questions
Know More about
Staff Selection Commission Combined High ...
Result | Eligibility | Application | Admit Card | Answer Key | Preparation Tips | Cutoff
Get Updates Brochure
Your Staff Selection Commission Combined Higher Secondary Level Exam brochure has been successfully mailed to your registered email id “”.
