SOLUTION: The sum of the reciprocals of two numbers is 16/15 and the second number is 1 larger thank the first. Find the two numbers?

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Question 540359: The sum of the reciprocals of two numbers is 16/15 and the second number is 1 larger thank the first. Find the two numbers?
Answer by oberobic(2304)   (Show Source): You can put this solution on YOUR website!
The two numbers can be defined as:
x
x+1
.
so their reciprocals are:
1/x
1/(x+1)
.
1/x + 1/(x+1) = 16/15
.
((x+1)+x)/(x*(x+1) = 16/15
.
15((x+1)+x) = 16(x*(x+1))
.
15x + 15 + 15x = 16(x^2 +x)
.
30x + 15 = 16x^2 +16x
.
0 = 16x^2 -14x -15
.
16x^2 -14x -15 = 0
.
(16x+10)(x-3/2) = 0
.
Check with FOIL.
16x^2 -24x +10x -15
Correct
.
So, x = -5/8 or x=3/2
.

.
Or you could solve with quadratic equation.
.
Solved by pluggable solver: SOLVE quadratic equation with variable
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=1156 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 1.5, -0.625. Here's your graph:
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