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Sum of a fraction and thrice of its reciprocal is 73/20. What is the fraction?

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Sum of a fraction and thrice of its reciprocal is 73/20. What is the fraction?
1). 4/5
2). 9/4
3). 4/9
4). 5/4


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Answered by on | Votes 2 |

Let the fraction be x.

Reciprocal = 1/x

Then,

x + 3/x = 73/20

⇒ x2 + 3 = 73x/20

⇒ 20x2 – 73x + 60 = 0

⇒ x = {- (-73) + √ (5329 – 4800)}/40     or        x = {- (-73) - √ (5329 – 4800)}/40

⇒ x = 96/40 = 12/5                                or        x = 50/40 = 5/4

∴ the required fraction is 5/4 or 12/5.

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