Пікірлер

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  @tejpalsingh366Күн бұрын

  Unnessory leanthy

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  @vannkan81526 күн бұрын

  I like this solution. make more videos

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  @matholympiadonlinesolver6 күн бұрын

  Thank

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  @vannkan81526 күн бұрын

  Cool

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  @minxythemerciless8 күн бұрын

  m = 2004 and n = 2005 are obvious solutions.

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  @mithunarora10 күн бұрын

  4009 is the other trivial solution

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  @yodaami20 күн бұрын

  What age Olympiad would that one be in? 60 yr old woman who did maths A level at school 40 years ago, feeling quite pleased to get this one easily.

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  @matholympiadonlinesolver20 күн бұрын

  It is for the lower class.

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  @yodaami16 күн бұрын

  @@matholympiadonlinesolver age? 7,8,9, 10, 11?

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  @matholympiadonlinesolver16 күн бұрын

  @@yodaami yes it is for 10 years old

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  @nexio545425 күн бұрын

  With small numbers like this, you can just list perfect squares under 45 and find by try and error. I solved it in 15 seconds like this :))

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  @MrRedEngineer25 күн бұрын

  I agree. But I don't agree with that mention how fast you solve buddy. Lower your ego and accept his solution.

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  @nexio545425 күн бұрын

  @@MrRedEngineer I accept his solution and it's definitely the most elegant solution. I didn't mean to show off and I'm sorry if my comment seems like I did. The problem being presented as an olympiad problem (which it clearly isn't), the goal would be to solve fast hence my solution and my exemple

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  @matholympiadonlinesolver25 күн бұрын

  Thank you

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  @kiloperson568025 күн бұрын

  Might I ask what country are you from?

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  @matholympiadonlinesolver25 күн бұрын

  I'm from cambodia

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  @kiloperson568023 күн бұрын

  @@matholympiadonlinesolver oh i asked because your pronunciation sounded like french to me haha, weird

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  @coderhub-tech794225 күн бұрын

  Tried calculating based off the thumbnail, i got c²-a² = -5 so (c+a)(c-a) = -5, using that and a little brute force, the 4 possible values are c = ±2, a = ±3. From there you get b = ±6 which is the solution

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  @matholympiadonlinesolver25 күн бұрын

  Ok thank you

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  @bledlbledlbledl25 күн бұрын

  the way i went about it was very similar to that. looking at the thumbnail, a² must be 5 more than c². starting from 1 and just squaring a few numbers, it didn't take long to notice that 3² was 5 more then 2². from there, finding b² was just a subtract

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  @Abby-hi4sf25 күн бұрын

  Always a+b > a-b , so you should not have four cases . I will assign the greater factor to the greater eqn

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  @coderhub-tech794225 күн бұрын

  Does not apply if b is negative, think again

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  @Abby-hi4sf25 күн бұрын

  @@coderhub-tech7942 Let us not forget that every negative number squared is always positive. All variable a, b, c, are sqared on the question So the answer is a= +/- 3 , b= +/- 6 and c= +/- 2

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  @coderhub-tech794225 күн бұрын

  @@Abby-hi4sf true, but you are factoring a²-c² or c²-a² depending on your approach, which can include negative numbers, so your argument doesn't work there

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  @Abby-hi4sf25 күн бұрын

  @@coderhub-tech7942 Whether you are factoring a²-c² or c²-a² , the fact remain that each variable is sqared .ex a²= (-a)² and (-c)² =c² so a²-c² = (-a)²-c² = a²-(-c)²

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  @honestadministrator27 күн бұрын

  writing z for sin^2 ( x) one gets f ( x) = (1 - z + z^2) /( z + ( 1 - z) ^2) = (1 - z + z^2) /( 1 - z + z^2) = 1

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  @matholympiadonlinesolver27 күн бұрын

  Nice

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  @vasilesinescu8428 күн бұрын

  How do you pronounce x?

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  @matholympiadonlinesolver28 күн бұрын

  What are you hearing?

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  @quelquun563329 күн бұрын

  One other way to see it is to know that sin^4 -cos^4= sin^2-cos^2. Then everything cancels out and you get the result.

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  @minakshisareeen1843Ай бұрын

  x is 3

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  @matholympiadonlinesolverАй бұрын

  Ok thank you

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  @davidsousaRJАй бұрын

  I did f(x) = (cos²x + sin²x.sin²x)/(sin²x + cos²x.cos²x) = (cos²x + sin²x.(1 - cos²x))/(sin²x + cos²x.(1 - sin²x)) = (cos²x + sin²x - sin²xcos²x))/(sin²x + cos²x - cos²xsin²x)) = (1 - sin²xcos²x)/(1 - sin²xcos²x) = 1. Very easy.

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  @matholympiadonlinesolverАй бұрын

  Nice

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  @tamarshahverdyan2723Ай бұрын

  98

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  @tamarshahverdyan2723Ай бұрын

  24

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  @edvinkarlsson9368Ай бұрын

  You messed up the x part, you somehow made it into /2(sqrt(5)+2) instead of 2(sqrt(5)+4)

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  @jwkim4428Ай бұрын

  derivative of f(x) is 0. f(x) is constant and f(0)=1. hence f (x)=1 for all x.

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  @matholympiadonlinesolverАй бұрын

  Ok thank you

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  @davidsousaRJАй бұрын

  @jwkim4428 how did you get thsi result? It is very tedious to calculate this derivative by the quotient rule, and there is no obvious term cancellation in the final result.

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  @rishabhraj3749Ай бұрын

  Bro.. Nice explanation

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  @matholympiadonlinesolverАй бұрын

  Thank you

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  @princesmith9212Ай бұрын

  So simple Well done

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  @matholympiadonlinesolverАй бұрын

  Thank you

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  @laseriitdАй бұрын

  first like

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  @matholympiadonlinesolverАй бұрын

  Thank you sir❤

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  @Redstoner34526Ай бұрын

  But arent there infinite solutions such as logbase2(10) for x and logbase3(3) for y or whatever other numbers you want that make 7

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  @Aksel37Ай бұрын

  But there is x=3 and y=0 to Can you explain me why do you don’t find it please

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  @matholympiadonlinesolverАй бұрын

  Probably I lost it thank

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  @thbb1Ай бұрын

  I have a slightly simpler path: sqrt(x) + sqrt(x-9) = 9 <=> sqrt(x)-9 = -sqrt(x-9) -> square both sides and develop x -18 sqrt(x) + 81 = x - 9 <=> 18 sqrt(x) = 90 <=> sqrt(x) = 90/18 = 5 => x=25.

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  @williams1045Ай бұрын

  Yep, 45^2/9^2=(45/9)^2=5^2=25

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  @matholympiadonlinesolverАй бұрын

  Ok thank🙏