Question : If $a + \frac{1}{a} = 8$ , then what is the value of $\frac{1}{a^{4}} + a^{4} ?$
Option 1: 4098
Option 2: 3846
Option 3: 3842
Option 4: 4094

Question

Question : If $a + \frac{1}{a} = 2$ and $b + \frac{1}{b} = - 2$ , then what is the value of $a^{2} + \frac{1}{a^{2}} + b^{2} + \frac{1}{b^{2}} ?$

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Answer 1

Correct Answer: 3842

Solution : $(a + \frac{1}{a}) = 8$
Squaring both sides, we get,
⇒ $(a^{2} + \frac{1}{a^{2}}) + 2 = 64$
⇒ $(a^{2} + \frac{1}{a^{2}}) = 62$
Squaring both sides again, we get,
⇒ $a^{4} + \frac{1}{a^{4}} + 2 = 3844$
⇒ $a^{4} + \frac{1}{a^{4}} = 3844 - 2$
⇒ $a^{4} + \frac{1}{a^{4}} = 3842$
Hence, the correct answer is 3842.

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Question : If a+1a=8, then what is the value of 1a4+a4?Option 1: 4098Option 2: 3846Option 3: 3842Option 4: 4094

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Question : If $a + \frac{1}{a} = 8$ , then what is the value of $\frac{1}{a^{4}} + a^{4} ?$
Option 1: 4098
Option 2: 3846
Option 3: 3842
Option 4: 4094