Explanation

x + 1/x = 26/5 gives 5x² − 26x + 5 = 0, with discriminant 26² − 4·5·5 = 676 − 100 = 576 = 24² > 0. A positive discriminant means two distinct real roots, and neither is zero (x = 0 is excluded by 1/x). Hence two such numbers exist. The answer is (C).