What is the value of u ?
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. 9725
- B. 6971
- C. 6726
- D. 6725 ✓
Correct Answer: D. 6725
Explanation
Expanding \( (\sqrt{2}+1)^{10} + (\sqrt{2}-1)^{10} \) yields \( 2(32 + 720 + 1680 + 840 + 90 + 1) = 6726 \). So \( u + f + v = 6726 \). Since \( f + v = 1 \), \( u = 6725 \).
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