Question : If $x$4 + $x$ -4 = 194, x > 0, then what is the value of $x+\frac{1}{x}+2$?
Option 1: 8
Option 2: 14
Option 3: 6
Option 4: 4
Correct Answer: 6
Solution : Given: $x^4+x^{-4}=194$ ⇒ $x^4+\frac{1}{x^4}=194$ Adding 2 both sides, we get: ⇒ $x^4+\frac{1}{x^4}+2=194+2$ ⇒ $(x^2+\frac{1}{x^2})^2=196$ ⇒ $x^2+\frac{1}{x^2}=14$ Adding 2 both sides, we get: ⇒ $x^2+\frac{1}{x^2}+2=14+2$ ⇒ $(x+\frac{1}{x})^2=16$ ⇒ $x+\frac{1}{x}=4$ Now, $x+\frac{1}{x}+2$ = 4 + 2 = 6 Hence, the correct answer is 6.
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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
Question : If $x^4+x^{-4}=47, x>0$, then what is the value of $x+\frac{1}{x}-2?$
Option 1: 1
Option 2: 0
Option 3: 5
Option 4: 3
Question : If $x^2+\frac{1}{x^2}=\frac{7}{4}$ for $x>0$, what is the value of $(x^3+\frac{1}{x^3})$?
Option 1: $\frac{3\sqrt{3}}{5}$
Option 2: $\frac{3\sqrt{15}}{5}$
Option 3: $\frac{3\sqrt{15}}{8}$
Option 4: $\frac{3\sqrt{5}}{8}$
Question : If $\frac{x^8+1}{x^4}=14$, then the value of $\frac{x^{12}+1}{x^6}$ is:
Option 1: 16
Option 3: 52
Option 4: 64
Question : If $x^2+\frac{1}{x^2}=\frac{7}{4}$ for $x>0$; then what is the value of $x+\frac{1}{x}$?
Option 1: $2$
Option 2: $\frac{\sqrt{15}}{2}$
Option 3: $\sqrt{5}$
Option 4: $\sqrt{3}$
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