SOLUTION: find two consecutive positive odd integers given that the sum of their reciprocal is 24/143

Question 953711: find two consecutive positive odd integers given that the sum of their reciprocal is 24/143
Answer by macston(5194) (Show Source): You can put this solution on YOUR website!
n=first integer; n+2=second integer
Find common denominator
Multiply each side by 143(n)(n+2)

Subtract (286n+286) from each side.

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=84100 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 11, -1.08333333333333. Here's your graph:

ANSWER 1: The first integer is 11
n+2=13 ANSWER 2: The second integer is 13
CHECK:

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