Question : If $x^{2}+\frac{1}{x^{2}}=1$, then, what is the value of $x^{48}+x^{42}+x^{36}+x^{30}+x^{24}+x^{18}+x^{12}+x^{6}+1$?
Option 1: – 9
Option 2: 0
Option 3: 1
Option 4: 9
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: 1
Solution :
Given: $x^{2}+\frac{1}{x^{2}} = 1$
Adding 2 on both sides, we get,
$x^{2} + \frac{1}{x^{2}} + 2 = 1 + 2$
⇒ $x^{2} + \frac{1}{x^{2}} + 2×x^2×\frac{1}{x^{2}} = 3$
⇒ $(x + \frac{1}{x})^{2} = 3$
$x + \frac{1}{x} = \sqrt3$
Cubing both sides, we get,
⇒ $(x + \frac{1}{x})^{3} = (\sqrt3)^2$
⇒ $x^{3} + \frac{1}{x^{3}} + 3x\times\frac{1}{x}(x + \frac{1}{x})= 3\sqrt3$
⇒ $x^{3} + \frac{1}{x^{3}} = 0$
⇒ $x^{3} = – \frac{1}{x^{3}}$
⇒ $x^{6} = -1$
Putting values of x
6
= –1,
$x^{48} + x^{42} + x^{36} + x^{30} + x^{24} + x^{18} + x^{12} + x^{6} + 1$
= $1 - 1 + 1 -1 + 1 -1 + 1 -1 + 1$
= 1
Hence, the correct answer is 1.
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 “”.
