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Question

Find three positive integers in arithmetic progression such that the sum of every two is a perfect square .

A
62,82,99
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B
60,84,102
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C
52,86,108
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D
None of these
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Solution

The correct option is D None of these
Let ad,a,a+d are positive integers in A.P.
Let m2=2ad,n2=2a+d,k2=2a
m2,k2,n2 are in A.P. with common difference 'd'
d=n2m22 (Or)n2k2 (Or) m2k2
a=k22
m2+n24
ad=k2n2+m22
a,d are integers m,n,k
Minimum values possible are m=2,n=14,k=10
ad=100196+4246<0
But ad must be positive
There is no such positive integer in A.P. whose sum taken two at a time are perfect squares in A.P.

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