Question

The sum of squares of two consecutive odd whole numbers is $34$. Find the numbers.

Answer 1

Let the numbers be $a-1,a+1$

${(a-1)}^2+{(a+1)}^2=34a^2+1-2a+a^2+1+2a=342a^2+2=342a^2=32a^2=16a=\pm 4$

$\therefore$ numbers are $4-1,4+1$ or $-4-1,-4+1$

$3,5$ or $-5,-3$