Question 674341
Let the consecutive integers be {{{ n }}} and {{{ n + 1 }}}
given:
{{{ n^2 + ( n + 1 )^2  = 145 }}}
{{{ n^2 + n^2 + 2n + 1 = 145 }}}
{{{ 2n^2 + 2n - 144 = 0 }}}
{{{ n^2 + n - 72 = 0 }}}
I can see that this is
{{{ ( n + 9 )*( n - 8 ) = 0 }}}
{{{ n = 8 }}} is the positive answer
{{{ n + 1 = 9 }}}
The numbers are 8 and 9
check:
{{{ 8^2 + 9^2 = 64 + 81 }}}
{{{ 64 + 81 = 145 }}}
OK