Question : If $x+\frac{1}{x}=-2$, then what is the value of $x^7+x^{-7}+x^2+x^{-2} ?(\mathrm{x}<0)$
Option 1: 4
Option 2: 2
Option 3: 1
Option 4: 0
New: SSC CHSL tier 1 answer key 2024 out | 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: 0
Solution :
$x+\frac{1}{x}=-2$
$⇒x^2+1=-2x$
$⇒x^2+2x+1=0$
$⇒(x+1)^2 = 0$
$\therefore x = -1$
By putting $x=-1$, we get,
$x^7+x^{-7}+x^2+x^{-2}=(-1)^7+(-1)^{-7}+(-1)^2+(-1)^{-2} = -2+2 = 0$
Hence, the correct answer is 0.
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 “”.
