Respuesta :

let one integer be x, the consecutive odd integer is x+2
reciprocals are 1/x and 1/(x+2)
1/x +1/(x+2)=24/143
make the denominators the same:
(x+2)/[x(x+2)] +x/[x(x+2)]=24/143
143(2x+2)=24(x)(x+2)
286x+286=24x²+48x
24x²-238x-286=0
use the quadratic formula: x=22 this doesn't work because 22 is not an odd number.
or x=-2.1666666666 (this is not an integer)

weird.
abidemiokin

The two numbers will be 22 and 24

  • Let the two consecutive odd integers be x and x+2

  • Their reciprocals will be 1/x and 1/x+2

If the sum of the reciprocals of two consecutive odd integers is 24/143, then;

[tex]\frac{1}{x} + \frac{1}{x+2} = \frac{24}{143}\\\frac{x+2+x}{x(x+2))} = \frac{24}{143}\\\frac{2x+2}{x(x+2))} = \frac{24}{143}\\[/tex]

Cross multiply

24x² + 48x = 286x + 286

24x² - 238x - 286 = 0

On factorizing, the value of x is 22

Hence the two numbers will be 22 and 24

Learn more on equations here: https://brainly.com/question/2972832

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