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
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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