For 1/3 < x < y < 2, which of the following statements is/are always correct? I. x + 1/x < y + 1/y II. √(1+y²)/y < √(1+x²)/x Select the answer using the code given below.

Consider f(t) = t + 1/t. Its derivative is 1 - 1/t², which is negative for t<1 and positive for t>1. So f is not monotonic on (1/3, 2) — it decreases then increases. Counter-example: x=0.5, y=1.5: x+1/x = 0.5+2 = 2.5; y+1/y = 1.5+0.667 ≈ 2.167. Here x+1/x > y+1/y, so Statement I is not always true. For Statement II, consider g(t) = √(1+t²)/t = √(1/t² + 1). As t increases, 1/t² decreases, so g(t) decreases. Since x < y, g(x) > g(y), i.e., √(1+x²)/x > √(1+y²)/y, which means √(1+y²)/y < √(1+x²)/x. So Statement II is always correct.