We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.
 
+0  
 
0
63
2
avatar+25 

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

\(\frac{1}{x}+\frac{1}{x+2}=\frac{9}{40}\)

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

 Jun 6, 2019
 #1
avatar+17774 
+1

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 
+1

\(\frac{1}{x}+\frac{1}{x+2}=\frac9{40}\\ \frac{x+2+x}{x(x+2)}=\frac{9}{40}\\ \frac{2x+2}{x^2+2x}=\frac{9}{40}\\ 9x^2+18x=80x+80\\ 9x^2-62x-80=0\\ (9x+10)(x−8)=0\\ x_1=\frac{-10}{9}, x_2=8\)

only 8 is an integer. 

 Jun 6, 2019
edited by GYanggg  Jun 6, 2019

6 Online Users

avatar
avatar