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(52800) (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
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sum of its reciprocal is 103 --- the 2 reciprocals?
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find the number --- which one of them?
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x + y = 15 --> y = 15-x
1/x + 1/y = 103 --> (x+y)/xy = 103
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(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:

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