Question : If $x^4+\frac{16}{x^4}=15617, x>0$, then find the value of $x+\frac{2}{x}$.
Option 1: $\sqrt{121}$
Option 2: $\sqrt{129}$
Option 3: $\sqrt{123}$
Option 4: $\sqrt{127}$
Correct Answer: $\sqrt{129}$
Solution :
Given: $x^4+\frac{16}{x^4}=15617$
⇒ $(x^2)^2 + (\frac{4}{x^2})^2 + 2\times x^2 \times \frac{4}{x^2} = 15617 + 2\times x^2 \times \frac{4}{x^2}$
⇒ $(x^2+\frac{4}{x^2})^2 = 15625$
⇒ $x^2 + \frac{4}{x^2} = 125$
⇒ $x^2 + (\frac{2}{x})^2 + 2\times x \times \frac{2}{x} = 125 + 2\times x\times \frac{2}{x}$
⇒ $(x+\frac{2}{x})^2 = 129$
⇒ $x+\frac{2}{x} = \sqrt{129}$
Hence, the correct answer is $\sqrt{129}$.
Related Questions
Know More about
Staff Selection Commission Combined Grad ...
Result | Eligibility | Application | Selection Process | Preparation Tips | Admit Card | Answer Key
Get Updates Brochure
Your Staff Selection Commission Combined Graduate Level Exam brochure has been successfully mailed to your registered email id “”.
Upcoming Exams
Trending Articles around SSC CGL
