IIT JEE , AIEEE Forum - Mathematics , Algebra

sandeepramesh

another method that struck me immediately at that time was this
EDIT: There was a typo, it shd be sec^2yi

Put $x_{i} = i^2 cdot sec {y_{i}}$

$implies 1^2 cdot an {y_{1}} + 2^2 cdot an {y_{2}} + cdots + n^2 cdot an {y_{n}} =$
$rac {1}{2} cdot (1^2 cdot sec^2 {y_{1}} + 2^2 cdot sec^2 {y_{2}} +cdots+ n^2 cdot sec^2 {y_{n}})$

$implies 1^2 cdot an {y_{1}} + 2^2 cdot an {y_{2}} + cdots + n^2 cdot an {y_{n}} =$
$rac {1}{2} cdot ( 1^2 cdot (1 + an ^2 {y_{1}}) + 2^2 cdot (1 + an ^2 {y_{2}}) + cdots + n^2 cdot (1 + an ^2 {y_{n}}))$

as tanyi can be random, compare coeffs to get tanyi = 1 and hence xi = i^2 :)

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