Answer:
3 and 5
Step-by-step explanation:
consecutive odd numbers have a difference of 2 between them.
let the consecutive odd numbers be n and n + 2, then
the reciprocals are [tex]\frac{1}{n}[/tex] and [tex]\frac{1}{n+2}[/tex]
The difference between the reciprocals is then
[tex]\frac{1}{n}[/tex] - [tex]\frac{1}{n+2}[/tex] = [tex]\frac{2}{15}[/tex]
combine the fractions into a single fraction
[tex]\frac{n+2-n}{n(n+2)}[/tex] = [tex]\frac{2}{15}[/tex]
[tex]\frac{2}{n+2}[/tex] = [tex]\frac{2}{15}[/tex] ( cross- multiply )
2n(n + 2) = 30 ( divide both sides by 2 )
n(n + 2) = 15
n² + 2n - 15 = 0 ← in standard form
(n + 5)(n - 3) = 0 ← in factored form
equate each factor to zero and solve for n
n + 5 = 0 ⇒ n = - 5
n - 3 = 0 ⇒ n = 3
but n > 0 ⇒ n = 3
The 2 integers are n = 3 and n + 2 = 3 + 2 = 5
