i dont get mhy you keep expanding things like (a+b) (a+b) into a(a+b) + b(a+b). why dont you just use FOIL (multiply the front terms, outisde terms, inside terms, last terms)
...I imagine some solvers would have soon stumbled across (3, 3, 1) or a permutation for the (x, y, z) triple in last problem, noting with relief that the first two equations are indeed true, then gleefully noting the arithmetic mean = (9 + 3 + 3) / 3 = 5.
...an elegant solution to that first problem...totally avoiding calculus....and reminding me of grouping terms and constants to "build" perfect squares for deriving equations of circles. Meanwhile, if one kept building the "T-table" of y values for consecutive negative values of x, those y-values get smaller...but more slowly...the differences between each y decrease by 2, starting with differences of 9 and 7, then: y=21, 12, 5, 0, -3, -4 (aha!), then the rebound: -3, 0, 5, 12, 21,...
This video is very impressive, but sometimes i think that when i see these types of problems that i could use a short-cut. but I'm guessing that you have to do it the long and smart way each time right?
you are awsome! thanks for the help. i'm sure that i can at least get into individuals in mathcounts now!
stevenman8 1 month ago
please disregard my last comment. i see why now
this is really helpful
stevenman8 1 month ago
i dont get mhy you keep expanding things like (a+b) (a+b) into a(a+b) + b(a+b). why dont you just use FOIL (multiply the front terms, outisde terms, inside terms, last terms)
stevenman8 1 month ago
...I imagine some solvers would have soon stumbled across (3, 3, 1) or a permutation for the (x, y, z) triple in last problem, noting with relief that the first two equations are indeed true, then gleefully noting the arithmetic mean = (9 + 3 + 3) / 3 = 5.
jwm239 1 month ago
...an elegant solution to that first problem...totally avoiding calculus....and reminding me of grouping terms and constants to "build" perfect squares for deriving equations of circles. Meanwhile, if one kept building the "T-table" of y values for consecutive negative values of x, those y-values get smaller...but more slowly...the differences between each y decrease by 2, starting with differences of 9 and 7, then: y=21, 12, 5, 0, -3, -4 (aha!), then the rebound: -3, 0, 5, 12, 21,...
jwm239 1 month ago
This video is very impressive, but sometimes i think that when i see these types of problems that i could use a short-cut. but I'm guessing that you have to do it the long and smart way each time right?
rubixpuzzlechamp 1 month ago
haha, you are awesome!!! since the mathcounts competition is almost coming, you video seems so helpful to me!!!! thank you so much. !!!!
117117nobody 2 months ago
Thanks!!!
mathcountsFTW 2 months ago
Yay!!
TanksPokemon 2 months ago