Question

Find two positive integers such that the square of one exceeds the square of the other by $105$.

Answer 1

Let one integer is $x$ and another $y$

then $x^2-y^2=105$

By trial and error

for $x=11$

$121-y^2=105$

$⟹y^2=16$

$y=4$

$\therefore$ two integers are $(11,4)$