Question

If 𝑎, 𝑏 are positive integers such that $a<b$ and $\left[\begin{array}{c}ab\end{array}\right]$
$\left[\begin{array}{c}a\\ b\end{array}\right]$=25, then (𝑎, 𝑏)= \)

Answer 1

$\because \left[\begin{array}{c}ab\end{array}\right]\left[\begin{array}{c}a\\ b\end{array}\right]$=25
$\Rightarrow a^2+b^2=25\dots \left(1\right)$
Since 𝑎 and 𝑏 are positive integer and 𝑎<𝑏,
so 𝑎=3 and 𝑏=4
$\Rightarrow (a,b)=(3,4)$