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many pairs of natural numbers

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by ajith » Wed Apr 21, 2010 1:25 am
gmatmachoman wrote:How many pairs of natural numbers are there the difference of whose squares is 45?


a)0 b)1 c) 2 d) 3 e) none of these
a^2 -b^2 = 45

(a+b)(a-b) = 45

45 = 45*1 or 9*5 or 15*3

if a+b =45
and a-b = 1
a = 23 and b = 22

if a+b = 9
and a-b = 5
a = 7 and b = 2

if a+b =15 and
a-b = 3
a= 9 and b = 6

So there are clearly 3 pairs of natural numbers which satisfy this
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by liferocks » Wed Apr 21, 2010 1:27 am
we are looking for solution of a^2-b^=45
or (a+b)(a-b)=45
now 45 can be split into 2 factors in 3 ways
1 45
3 15
5 9
taking each pair we get following solutions
a+b a-b a b
45 1 23 22
15 3 9 6
9 5 7 2

hence ans is 3 option D
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