if 1/x + 1/y = 1/205 then possible no. of integral pairs of (x,y) will be. where x and y are positiv

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04 Apr 2012 integral pair

if 1/x + 1/y = 1/205 then possible no. of integral pairs of (x,y) will be. where x and y are positive integer.

OPtion

1) 1
2) 2
3) 3
4) 4
5) 5
6) 6
7) 7
8) 8
9) 9
10) none of these

Solution

1/x + 1/y = 1/205
on solving we get y = 205x/(x-205),
note that factor of 205 are 1, 5, 41, 205
now possible values of x for getting integral y are
205+1, 205+5, 205+41, 2*205, 6*205, 42*205, 206*205

Correct Option: 7 Best Solution (1)

Viru Sihag   12 years AGO

First of all assume that the value of x=410 and put in the equation xy/205=x+y then the value of y=410
Trick is that first multiply 205 by n+1 and divide by n is equal to integer then this is a solution. So first i take n=1 then this is an integer and then n=2 then its not an integer so its not an answer of this. n=1,n=5,n=41 these are the 5 ans.
The pair of (x,y) is (410,410),,(1230,246),,(246,1230),,(8610,210)& (210,8610) and 2 more solutions are- (206,42230) & (42230,206)

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