Consider the following statements: I. (u + v + f) is an integer. II. (f + v) is an integer. [Given: u is a positive integer, 0 < f < 1 is a real number, (√2 + 1)¹⁰ = u + f and (√2 - 1)¹⁰ = v]. Which of the above statements is/are correct?
A.I only
B.II only
C.Both I and II✓ Correct
D.Neither I nor II
Explanation
(√2+1)¹⁰ + (√2-1)¹⁰ is an integer (since odd powers of √2 cancel out). So u + f + v = integer, meaning f + v is also an integer (since u is integer). Both statements I and II are correct.
💡 Practice unlimited NDA PYQs + AI-tracked progress on each topic. Sign up free →