Need $49^2-98a$ to be a square number
$=49(49-2a)\\
=7^2(49-2a)$
$\therefore 49-2a$ is also a square number, and it is odd$-$even$=$odd
Odd squares below $49:$
$25\ \ \Rightarrow b^2=7^2\times25\Rightarrow b=35\\
9\ \ \Rightarrow b^2=7^2\times9\Rightarrow b=21\\
1\ \ \Rightarrow b^2=7^2\times1\Rightarrow b=7$