What is the value of uv ?
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. 1
- B. 2
- C. \( 0 < uv < 1 \) ✓
- D. \( 1 < uv < 2 \)
Correct Answer: C. \( 0 < uv < 1 \)
Explanation
Multiplying gives \( (u+f)v = 1 \), which means \( uv = 1 - fv \). Since \( 0 < f < 1 \) and \( 0 < v < 1 \), \( fv \) is between 0 and 1. Thus, \( uv \) is strictly between 0 and 1.
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