Art of Problem Solving: 2012 AMC 10 A #22

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  • Опубліковано 24 жов 2024

КОМЕНТАРІ • 21

  • @ArtofProblemSolving
    @ArtofProblemSolving  12 років тому +6

    @flareashes Plain old TV. Magic fingers. (And a touch-screen overlay.)

  • @ArtofProblemSolving
    @ArtofProblemSolving  12 років тому +5

    @PokemonSucks7 No, I'm pretty sure it's 847...

  • @flareashes
    @flareashes 12 років тому +2

    What type of board is that?

  • @ArtofProblemSolving
    @ArtofProblemSolving  12 років тому +3

    @PokemonSucks7 That's 1-4(212-m^2) = 4m^2 - 847.... There's more in that discriminant than just 4(212-m^2)!

  • @ZelongDong
    @ZelongDong 12 років тому

    @ArtofProblemSolving 4(212-M^2)=848-4M^2 since 212*4=848

  • @adilbhatti6299
    @adilbhatti6299 5 років тому

    AWESOME!

  • @ZelongDong
    @ZelongDong 12 років тому

    @ArtofProblemSolving he did the 1- afterwards again

  • @louisliu56
    @louisliu56 3 роки тому +1

    he probably has a secret way to write on the board

  • @זאבגלברד
    @זאבגלברד 6 років тому

    use the known formula for the sum of an arithmetic ... For those that this is simpler to figure m*m etc...

  • @ZelongDong
    @ZelongDong 12 років тому

    @ArtofProblemSolving well he 1-c which c =4(212-m^2) later on

  • @LifeIsBeautiful-ki9ky
    @LifeIsBeautiful-ki9ky 4 роки тому

    4×212 =848 not 847.

  • @victorialiao4695
    @victorialiao4695 3 роки тому

    wow you got into mop!!

  • @pedroduarte6672
    @pedroduarte6672 8 років тому

    If I understand the question correctly.The answer cannot be an odd number, since the sum of even numbers cannot deliver a odd number, even if number of even numbers summed was odd. 2+4+6=6+6=12 So the answer could only be 256 or 258.

    • @helenee510
      @helenee510 7 років тому +1

      Well, the question is asking for all the possible values of n (to be more precise, their sum), while you seem to understand it as the sum of first n positive integers.

    • @pedroduarte6672
      @pedroduarte6672 7 років тому

      However, the n numbers must be even integers. The sum of even integers is always even.

    • @camelliaguan6388
      @camelliaguan6388 7 років тому +1

      The question is asking for the possible values of n. The question is asking for the first n positive integers. It could be asking for the first 5 positive even integers, and they would be 2, 4, 6, 8, and 10. While even integers will always add up to an even number, it is asking for the number of even integers. This number does not always have to be even.

    • @camelliaguan6388
      @camelliaguan6388 7 років тому +1

      The question is also asking for the sum of possible values of n. This doesn't necessarily have to be even since as I said before, the number of even integers can be any number. In the first comment of yours, you put: 2+4+6=6+6=12. There are 3 starting even integers, and this number is odd.

    • @ayoubmenia9182
      @ayoubmenia9182 5 років тому

      @@camelliaguan6388 so what abt (m square ) why didn't he use directly m ??

  • @ZelongDong
    @ZelongDong 12 років тому

    he messed up bad
    it's not 847 its 848