Let the number we have to find be N.

The sum of the number and its reciprocal is 13/6

=> N + 1/N = 13/6

=> N^2 + 1 = (13/6)N

=> 6N^2 + 6 = 13N

=> 6N^2 - 13N + 6 = 0

=> 6N^2 - 9N -...

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Let the number we have to find be N.

The sum of the number and its reciprocal is 13/6

=> N + 1/N = 13/6

=> N^2 + 1 = (13/6)N

=> 6N^2 + 6 = 13N

=> 6N^2 - 13N + 6 = 0

=> 6N^2 - 9N - 4N + 6 = 0

=> 3N(2N - 3) - 2(2N - 3) = 0

=> (3N - 2)(2N - 3) = 0

=> N = 2/3 and 3/2

**The required number is 2/3 or 3/2**