Question

For two positive integers $a,b$ if $a^2-b^2=7$ find the value of $a,b$.

Answer 1

Given for two positive integers $a,b$,

$a^2-b^2=7$

or, $(a+b).(a-b)=7.1$

$\Rightarrow (a+b)=7$......(1) and $(a-b)=1$......(2) [ Since $a,b$ are positive integers].

Solving from (1) and (2) we get,

$a=4,b=3$.