i can understand mandarin chinese as a korean better than i can comprehend that

ahhh basically for x^3-x-1=0, you substitute a-k/a for x
then you expand the terms & combine similar terms
and you substitute 1/3 for k because k can be anything to cancel out terms, leaving you with a^3 + 1/27a^3 - 1 = 0
then you can solve-

for the tangent one, you start off with tan(x-y) and you add z so it includes all x, y, and z -> tan(x-z-y-z) -> tan((x-z)-(y-z))
and you cross multiply + use the fact that tangent is an odd function to remove negative signs and stuff

Oh wow that’s cute I didn’t know you could do that

ah yes it's an interesting way of solving