Help! Need ASAP Please! Problem: The sum of 2 times a number and 5 times its reciprocal is 23/3. Find the numbers.

Mathematics · College · Thu Feb 04 2021

Answered on

Let the number be x

Then, it's reciprocal is 1/x

Now, according to question 

2x + 5(1/x) = 23/3

(2x² + 5)/x = 23/3

Cross-Multiplying,  we get

6x² + 15 = 23x

6x² - 23x + 15 = 0

6x² - 18x - 5x + 15 = 0

6x(x - 3) - 5(x - 3) = 0

(6x-5) (x-3) = 0

6x - 5 = 0

6x = 5

x = 5/6

And, x - 3 = 0

x = 3

 

Hence, the possible numbers are 5/6 and 3.

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