Question : If $x^4+x^{-4}=194, x>0$, then the value of $x+\frac{1}{x}$ is:
Option 1: 14
Option 2: 6
Option 3: 4
Option 4: 8
Answer (1)
5th Jan, 2024
Correct Answer: 4
Solution :
$x^4+\frac{1}{x^4}=194$
⇒ $(x^2+\frac{1}{x^2})^2-2=194$
⇒ $(x^2+\frac{1}{x^2})^2=196$
⇒ $x^2+\frac{1}{x^2}=14$
⇒ $(x+\frac{1}{x})^2-2=14$
⇒ $(x+\frac{1}{x})^2=16$
$\therefore$ $x+\frac{1}{x}=4$
Hence, the correct answer is 4.
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