Finnish Math Olympiad | 2004 Q1 & Q2
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3 жыл бұрынWe present solutions to two questions from the 2004 Finish math olympiad. One involves roots of quadratic polynomials and the quadratic formula. The other involves a bit of manipulation inside of Q[sqrt(3)].
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@siddharthpuranam 3 жыл бұрын
Guess these two are the easiest problems ever featured on this channel :)
@dhruvanaidu9738 3 жыл бұрын
just replace the b^2 with ac in the final fraction and the numerator simplifies to (a+c)^2 -ac which is (a+c)^2-b^2. so now its just difference of squares
@jonathanweihing9650 3 жыл бұрын
Nice video. I like the Math olympiad question/videos. They are always great.
@goodplacetostop2973 3 жыл бұрын
9:49
@caesar_cipher 3 жыл бұрын
Math flex by Michael from
@me2ntomori280 3 жыл бұрын
日本人です。聞き取りやすい英語で助かっています。いつも大変参考になる数学の動画をありがとうございます。
@GraemeMcRae 3 жыл бұрын
It’s interesting to note that if nonzero integers a, b, and c are in geometric progression then (a^2+b^2+c^2)/(a+b+c) is an integer.
@soumitrapharikal5503 3 жыл бұрын
Great Work Sir...Keep Working hard.
@L4wLiP0p 3 жыл бұрын
For the second problem, another approach is noticing that for (a*sqrt(3)+b)/(b*sqrt(3)+c) to be rational, we must have b=q*a and c=q*b for some rational number q.
@kakalibiswas1312 3 жыл бұрын
Watching the olympiad question solution is so eye soothing
@garvittiwari11a61 3 жыл бұрын
Please create a series for math Olympiad, I like your problem solving tecgniques
@josephmartos 3 жыл бұрын
First time I got to solve some of your problems. They were not too hard though, but i am still very excited hahha
@naveensurya5956 3 жыл бұрын
Nice solution
@masoncamera273 3 жыл бұрын
Damn this is a math teacher who lifts
@Goku_is_my_idol 3 жыл бұрын
Otherwise if b²=ac and all belong to N we can say that all are in geometric series a,ar,ar² then simplify to get the ans.
@brendawilliams8062 3 жыл бұрын
Thankyou.
@leonardocoroneo6344 3 жыл бұрын
Beautiful proofs
@michelsantana2642 3 жыл бұрын
sooooo nice the second question!
@brendawilliams8062 3 жыл бұрын
Looks like a gravity or modified gravity to me. Your talent is above my experience.
@HemantPandey123 3 жыл бұрын
Just use a, ar, ar^2 as terms in GP and get answer in one step! (Due to the fact 1+r+r^2 is divisible by 1+r^2+r^4)
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