Question 733314
Call the consecutive integers {{{ n }}} and {{{ n+1 }}}
given:
{{{ n^2 + ( n + 1 )^2 = 61 }}}
{{{ n^2 + n^2 + 2n + 1 = 61 }}}
{{{ 2n^2 + 2n - 60 = 0 }}}
{{{ n^2 + n - 30 = 0 }}}
Looking at this, I see that {{{ 5*6 = 30 }}} and the difference is {{{ 6 - 5 =  1 }}},
so my guess is:
{{{ ( n + 6 )*( n - 5 ) = 0 }}}
{{{ n = -6 }}}
{{{ n = 5 }}} 
I need the positive solution
{{{ n + 1 = 6 }}}
The consecutive numbers are 5 and 6
check:
{{{ 5^2 + 6^2 = 25 + 36 }}}
{{{ 25 + 36 = 61 }}}
OK