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Grade: 12th pass

                        

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

6 years ago

Answers : (2)

Sher Mohammad
IIT Delhi
askIITians Faculty
174 Points
							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




6 years ago
mycroft holmes
272 Points
							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.
						
6 years ago
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