SOLUTION: the sum of two numbers is 15. sum of its reciprocal is 103 . find the number

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Question 1065801: the sum of two numbers is 15. sum of its reciprocal is 103 . find the number
Found 2 solutions by ikleyn, Alan3354:
Answer by ikleyn(52799)   (Show Source): You can put this solution on YOUR website!
.
x + y = 15,       

 = 103.   

---->  


x + y = 15,

 = 103.

---->


x + y = 15,

15/xy = 103,

---


x + y = 15,

xy = .

---->


x and y  are the roots of the quadratic equation

 = 0.

Now you solve this quadratic equation and find its solutions.

They are your x and y.


Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
the sum of two numbers is 15. sum of its reciprocal is 103 . find the number
----------
sum of its reciprocal is 103 --- the 2 reciprocals?
----------
find the number --- which one of them?
--------------
x + y = 15 --> y = 15-x
1/x + 1/y = 103 --> (x+y)/xy = 103
---
(x+y)/xy = 103
Sub for y
15/(x*(15-x)) = 103
15 = 1545x - 103x^2
103x^2 - 1545x + 15 = 0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation (in our case ) has the following solutons:



For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=2380845 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 14.9902849700154, 0.00971502998458411. Here's your graph:

======================
x = x1 value
y = x2 value
Or vice versa.


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