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The sum of the reciprocals of two consecutive even integers is 9/40 . This can be represented by the equation shown.

1x+1x+2=940

Use the rational equation to determine the integers. Show your work.

 Jun 6, 2019
 #1
avatar+23254 
+2

1/x  +  1/(x+2)  =  9/40

 

Multiply each term by the common denominator of  40(x)(x+2):

 

[1/x](40)(x)(x+2)  +  [1/(x+2)](40)(x)(x+2)   =  [9/40](40)(x)(x+2) 

 

40(x+2)  +  (40)(x)  =  9(x)(x+2)

 

40x + 80  +  40x  =  9x2 + 18x

                         0  =  9x2  -  62x  -  80

                         0  =  (9x + 10)(x - 8)                 

 

Disregarding the answer which is a fraction:

--->     x  =  8;  x + 2  =  10

 Jun 6, 2019
 #2
avatar+985 
0

1x+1x+2=940x+2+xx(x+2)=9402x+2x2+2x=9409x2+18x=80x+809x262x80=0(9x+10)(x8)=0x1=109,x2=8

only 8 is an integer. 

 Jun 6, 2019
edited by GYanggg  Jun 6, 2019

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