Question

Find two consecutive positive odd numbers, the sum of whose squares is $74.$

Answer 1

Let the two consecutive positive odd numbers are $n$ and $n+2$

Sum of their squares is $74$

So,

$n^2+(n+2{)}^2=74$

$n^2+n^2+4n+4=74$

$2n^2+4n-70=0$

$n^2+2n-35=0$

$n^2+7n-5n-35=0$

$n(n+7)-5(n+7)=0$

$(n-5)(n+7)=0$

$n=5$ or $n=-7$

as given in the problem, $n$ is a positive number

therefore $n=5$

and the numbers are $5$ and $7$