Mathematics: The sum of the reciprocals of two consecutive positive integers is 17/72 . write an equation that can be used to find the two integers. what are the integers? show work, somebody , it will be greatly appreciated!

The sum of the reciprocals of two consecutive

Ответ:

DASASDAEDWEDA

20.06.2020

Denote two consecutive positive integers by x and (x + 1).

$\frac{1}{x} + \frac{1}{x+1}= \frac{17}{72} 
\\72(x+1)+72x=17x(x+1)
\\72x+72+72x=17x^2+17x
\\17x^2-127x-72=0
\\a=17,b=-127,c=-72
\\x_{1,2}= \frac{-b \pm \sqrt{b^2-4ac} }{2a} = \frac{-(-127) \pm \sqrt{127^2-4(17)(-72)} }{2\times 17}= \frac{127 \pm 145 }{34}
\\x_1= \frac{127 + 145 }{34}=8
\\x_1= \frac{127 - 145 }{34}=- \frac{18}{34} 
$

Therefore, x = 8. The two consecutive integers are 8 and 9.

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Ответ:

EricBryanLopez

25.02.2021

Mathematics

the output is 4 less than the input."

Input, x 1 2 3 4
Output, y -3 -2 -1 0

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The sum of the reciprocals of two consecutive positive integers is 17/72 . write an equation that can be used to find the two integers. what are the integers?
show work, somebody , it will be greatly appreciated!

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