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
Answer (1)
22nd Jan, 2024
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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