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  4. For any positive odd integer n , n ( n 2-1) is divisible by

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Q. For any positive odd integer $n , n \left( n ^{2}-1\right)$ is divisible by

KCETKCET 2022

Solution:

given $2 y^{2}-3 x+6 y-1=0 \rightarrow(1)$
$\Rightarrow 4 y +4=0 $
$\therefore y =-1$ (by diff. wrt $y$ treating $x$ as constant)
$\therefore(1) \Rightarrow 2-3 x-4-1=0$
$ \therefore 3 x=-3$
$\therefore x=-1$