Question 540741
Call the consecutive odd numbers {{{n}}} and {{{n+2}}}
given:
{{{ n*( n + 2 ) = n^2 + 10 }}}
{{{ n^2 + 2n = n^2 + 10 }}}
Subtract {{{ n^2 }}} from both sides
{{{ 2n = 10 }}}
{{{ n = 5 }}}
{{{ n + 2 = 7 }}}
The numbers are 5 and 7
check:
{{{ 5*( 5 + 2 ) = 5^2 + 10 }}}
{{{ 5*7 = 25 + 10 }}}
{{{ 35 = 35 }}}
OK