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The sum of a number and its reciprocal is 2whole number 1 over 6. Find that number​

User Akshat Zala
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1 Answer

14 votes
14 votes

Answer:

2/3 or 3/2

Explanation:

Let x represent the number. The given relation is ...

x +1/x = 2 1/6

x^2 +1 = (13/6)x

6x^2 -13x +6 = 0 . . . . . subtract the right side and multiply by 6

(6x -9)(6x -4)/6 = 0 . . . . factor

(2x -3)(3x -2) = 0 . . . . . . simplify a bit

x = 3/2 or 2/3 . . . . . . . . values of x that make the factors zero

The number is 2/3 or its reciprocal, 3/2.

User Maxfowler
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