What is the multiplicative inverse of \( (\sqrt{2} + 1)^{20} \) ?
For the next five (05) items that follow : Let u be a positive integer and f be a real number lying between 0 and 1. Further, \( (\sqrt{2} + 1)^{10} = u + f \) and \( (\sqrt{2} - 1)^{10} = v \)
- A. v
- B. \( v^2 - 1 \)
- C. \( v^2 \) ✓
- D. \( v^2 + 1 \)
Correct Answer: C. \( v^2 \)
Explanation
The multiplicative inverse is \( (\sqrt{2} + 1)^{-20} \), which is equal to \( (\sqrt{2} - 1)^{20} \). Since \( v = (\sqrt{2} - 1)^{10} \), the inverse is \( v^2 \).
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