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find integral value of equation 1/x+1/y=1/2007

find integral value of equation 1/x+1/y=1/2007

Grade:12th pass

3 Answers

Sher Mohammad IIT Delhi
askIITians Faculty 174 Points
10 years ago
1/x=1/2007-1/y
1/x =(y-2007)/2007y
x=2007y/(y-2007)
for y=2008, x= 2007*2008, is one integral solution.

sher mohammad
b.tech, iit delhi




mycroft holmes
272 Points
10 years ago
Since x,y>2007 we have x = 2007+a, y = 2007+b for some naturals a,b So, 1/(2007+a)+1/(2007+b) = 1/2007. Cross multiplying etc. we get, ab = 2007^2 = 3^4 X 223^2 For any ordered pair of naturals a,b satisfying ab = 2007^2, we have the corresponding pair (x,y) = (2007+a, 2007+b) as a solution. e.g. a=b=2007 gives x=y=4014 or a=1, b = 2007^2 gives x=2008,y=2007*2008 All in all we get 29 ordered pairs as solutions.
Rokesh
13 Points
3 years ago
1/x + 1/y = 1/ c
1/(c+a)+a/(c*(c+a))=1/c
a can be any number you want
1/(2007+a) + a/(2007*(2007+a)) = 1/2007
Put any value for a,
x = 2007+a
y = a/(2007*(2007+a))                                                                   
-Rokesh M
 
 
 
 
 
 
 
 

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