SOLUTION: The sum of half number and its reciprocal is the same as 51 divided by the number. find the number.

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From the problem description, you can write:
n/2 + 1/n = 51/n where n is the unknown number. Multiply through by n to clear the fractions.
(n^2)/2 + 1 = 51 Now multiply through by 2.
n^2 + 2 = 102 Subtract 2 from both sides.
n^2 = 100 Take the square root of both sides.
n = +/- 10
Both 10 and -10 will work here.