Question

The sum of the squares of two consecutive positive odd numbers is 514. Find the numbers.

Answer 1

Let the two consecutive no. be x &x+2
A.T.Q
$x^2+(x+2{)}^2=514$
$x^2+x^2+4+4x=514$
$2x^2+4x=514-4$
$2x^2+4x=510$
$2x^2+4x-510$
$x^2+2x-255$
$x^2+17x-15x-255$
$x(x+17)-15(x+17)$
$(x+17)(x-15)$
$x+17=0$
$x=-17$
&
$x-15=0$
$x=15$
if the odd no. is
$x=-17x+2=-17+2x=-15$......
if the odd no. is
$x=15x+\mathrm{2..}x=15+2x=17$
those no. can be -17 or-15
or it can be 15 or 17