The sum of 2 numbers is 9. Eighteen times the sum of their reciprocals is also 9. Find the nummber
Answers
Answer is 6 or 3
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Concept
After initially accounting for any variable that relates to both numbers and after formulating the supplied condition in mathematical form, we will use the given condition to solve the resulting equation and determine the numbers.
Given
The summation of the numbers is= 9
Eighteen times of the sum to their reciprocals = 9
Find
We have to calculate the value of the variables.
Solution
Let x and y be the numbers that are given. Applying the aforementioned criteria leads to the result x + y = 9 (1)
Additionally, 18/x + 18/y = 9 or 1/x + 1/y = 1/2 can be used to express this.
(2)
The answer to equation (1) is y = 9 - x.
Following this, we have 1/x + 1/(9-x) = 1/2 (9-x+x)/[x*(9-x)] using equation (2).
=1/2 18 = 9x - x^2\sx^2 - 9x +18 = 0
Following factorization, we obtain (x - 3) (x - 6) = 0, where x = 3 and x = 6.
Using (1)'s x = 3 we obtain y = 6.
As a result, the variables have values of 3 and 6, respectively.
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