hello ladies and gentlemen welcome to princeton university and over there that's the oldest
building Nassau Hall and first of all i just want to mention that i'm not associated with princeton
in any way i'm not faculty i'm not a student here and they didn't invite me to here i just came
here by myself to enjoy this wonderful place and i'm very sorry there's a construction over there
hopefully it's not too bad yeah but anyway i want to tell you guys that a lot of colleges in the US
here they have students prepare math competitions for high school students and at Princeton they
have that as well so today i prepared two questions for you guys so let's take a look
this is the first one i have you see it i came here prepared print this out at home and then
it got here but anyway let me read the question for you guys it says let x and y be positive real
solutions satisfying this equation log x squared plus log y squared is equal to log of x squared
plus log of y squared and log base what doesn't really matter because we're going to compute the
maximum possible value for log of x y and then square so go ahead and pause the video and try
this this is from their 2019 algebra test and this is their logo done okay i have another question
and i love this question a lot first off we have a quadratic function x squared plus 4x plus 2
and then we will have an equation check this out f of f of f of f of x is equal to zero
and when you solve this equation we are going to get the biggest real solution and also the
smallest real solution we are going to let r be the difference between the biggest and also the
smallest real solution of that equation and once you find out what r is r will be in the form of
a to the power of p over q and right here it says a is square three meaning that it does
not have any perfect square as a factor besides one so 4 9 16 25 etcetera they are now factors of
a and then p q are relative d prime and they say that because we are going to compute a plus p plus
q in this particular form with these conditions so go ahead and try this right here as well
done cool all right unfortunately
i didn't bring my whiteboard to me but you know what i have this for you guys check this out i
gotta still [ __ ] and for all the files i will give you guys the link in the description okay
all right so for the long question the answer is 16
and then for the f of f of f of f of x that question is 35 all right
and let me just show you guys the test here it has eight questions on this page and then
the questions at the end man yeah these are pretty crazy you guys can you know take a look and try it
and personally i love solving math competition questions but i cannot solve all of them in
fact i can only solve some of them and sometimes there are questions that cannot even understand
what the questions are asking but whenever i can solve the question i will be super super
happy so that's just me and guests can tell me like how you are with like math competition
questions do you like that what your experience with them etc etc and yeah this is the test that
i have for you guys for today and of course princeton there are so many well-known people
well-known famous mathematicians from here and just to name a few albert einstein and
john nash from beautiful my and andrew wiles the one who solves the
vermont's last serum and then recently of course we can talk about professor terence
tao and also professor potion low and there are plenty more um if you guys know more of course
drop down your names yeah in the comment down below and if you happen to be a student here let
me know how do you like here yeah this is just such a wonderful place i'm so happy to be here
just to take a look and breathe the air so hopefully you guys like this video today i
will solve the questions for you guys later on once i get back home
all right so maybe i'll take you guys a little bit closer just to have a better view with the
with the building right here
oh
okay bye