This is from one of the Finnish national Math competitions MAOL http://www.maol.fi/fileadmin/users/K...vastaukset.pdf

prove that

$\displaystyle

\sqrt{17-12{\sqrt2}}-\sqrt{17+12{\sqrt2}}=6$

I have a question

1) The sample answer splits 17 into 9 and 8. Yet it moves the eight to the "ends" of the equation $\displaystyle \sqrt{9-12{\sqrt2}+8}-\sqrt{9+12{\sqrt2}+8}=6 $

Why is this?

Thank you!