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The sum of a number and its reciprocal is 2⅙.Find the number​

User Hyque
by
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1 Answer

4 votes

Answer:

2/3 or 3/2

Explanation:

If the number is x, and its reciprocal is 1/x, then:

x + 1/x = 2⅙

Convert mixed number to improper fraction:

x + 1/x = 13/6

Multiply both sides by 6x:

6x² + 6 = 13x

6x² − 13x + 6 = 0

Factor using AC method. 6×6=36. Factors of 36 that add up to -13 are -4 and -9. -4/6 and -9/6 reduce to -2/3 and -3/2.

(3x − 2) (2x − 3) = 0

Solve for x:

x = 2/3 or 3/2

Alternatively, you can use quadratic formula to solve for x.

User Dotrinh DM
by
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