WBCS.LIVE practice question

If a + \frac{1}{a} = 3, then (a^4 + \frac{1}{a^4}) = \wn

Solve this multiple-choice question and check the correct answer with its explanation below.

Answer options

  1. 77
  2. 47
  3. 81
  4. 27

Correct answer and explanation

Correct answer: 47

Explanation: āœ… Correct Answer: B) 47 šŸ“š Explanation: Squaring both sides of $a + 1/a = 3$ gives $a^2 + 1/a^2 + 2 = 9$, which means $a^2 + 1/a^2 = 7$. Squaring this result a second time yields $a^4 + 1/a^4 + 2 = 49$. Subtracting 2 from both sides gives the final value: $a^4 + 1/a^4 = 47$.