Question : If $a+\frac{1}{a}=3$, then the value of $a^4+\frac{1}{a^4}$ is:
Option 1: 48
Option 2: 81
Option 3: 27
Option 4: 47
Correct Answer: 47
Solution : Given, $(a + \frac{1}{a})$ = 3 Squaring both sides, we get, $(a + \frac{1}{a})^2 = (3)^2$ ⇒ $a^2 + \frac{1}{a^2} + 2 = 9$ ⇒ $a^2 + \frac{1}{a^2} = 7$ Squaring both sides, ⇒ $a^4 + \frac{1}{a^4} + 2 = 49$ $\therefore a^4 + \frac{1}{a^4}$ = 47 Hence, the correct answer is 47.
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