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
llm
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.