How Many Ways Can this be a Square?

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  • เผยแพร่เมื่อ 22 ธ.ค. 2024

ความคิดเห็น • 23

  • @WrathofMath
    @WrathofMath  29 วันที่ผ่านมา +4

    I'll be traveling for Thanksgiving soon, but I've tried to get ahead so daily videos will continue. Some quicker and easier discussions but I hope you'll find them fun nonetheless!
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  • @tomkerruish2982
    @tomkerruish2982 29 วันที่ผ่านมา +22

    Let a be an arbitrary nonzero integer and b equal to 0. Then (a³+b³)/(a-b) = a³/a = a².

  • @ARKGAMING
    @ARKGAMING 29 วันที่ผ่านมา +13

    6:17 b=0 a≠0 also works for the first question, it's just that it doesn't fit (mb, b) but (a³+0)/(a-0) =a²

  • @ethos8863
    @ethos8863 28 วันที่ผ่านมา +2

    I wove this guy's dry humor "... and let a be anything whatsoever" is so heat

  • @wyboo2019
    @wyboo2019 29 วันที่ผ่านมา +3

    dude you pump out videos faster than i can possibly watch them. in terms of math channels you are number 1 in output

    • @WrathofMath
      @WrathofMath  28 วันที่ผ่านมา +1

      I'm always grinding, got a fun paradox video lined up for tomorrow!

  • @TazPessle
    @TazPessle 28 วันที่ผ่านมา +4

    For the second example, if you use the same a=mb method,
    (m^2)(b^2) - mb^2 + b^2
    (b^2)(m^2 -m +1)
    Ie. m=1 is a solution for any b
    And we can ask at what values multiplying b^2 by (m^2 -m +1) produces a square. Well, all i could see is where
    b^2 = m^2 - m +1
    b^2 -1 = m^2 -m
    And without going further my gut says there are no more answers here (thinking about it as factors, I can't see another positive integer solution, but I'm not math-smart; i don't know why I'm watching this). Anyway,
    Soln: a = b or b=0.
    But the b=0 answer seems trivial. Especially as it works for the first question too as people have pointed out. Having a variable as zero just removes it and makes the formulation of the question redundant. Which is why i thought you avoided it. but then the second question it's what you gave.

    • @squirrelllllllllllllllllllllll
      @squirrelllllllllllllllllllllll 28 วันที่ผ่านมา +1

      i actually did the exact same thing as you and got the solution where m = 1. funny because our working out is basically exactly the same.

  • @cjaoun23240
    @cjaoun23240 29 วันที่ผ่านมา +4

    I love the nintendo music in the background

    • @WrathofMath
      @WrathofMath  28 วันที่ผ่านมา

      Classic tunes!

    • @timh2859
      @timh2859 28 วันที่ผ่านมา

      ​@@WrathofMathwhat's the song at the end right before the credits?

  • @robertethanbowman
    @robertethanbowman 27 วันที่ผ่านมา

    So there are so far two types of solutions, [b=0 and a = any integer other than zero] and [(a,b) = (2,1) and (4,2),... and (2n,n)].
    But are there other types of solutions, or can it be proven that there are not?

  • @at0micbunnygirl
    @at0micbunnygirl 29 วันที่ผ่านมา +3

    Shakespeare would have liked this problem... 2b or not 2b. 😜🤣

  • @mzg147
    @mzg147 28 วันที่ผ่านมา

    huh, but what about other pairs? Do any other pairs work? I wonder how hard this problem is

  • @EdMatthewMorales
    @EdMatthewMorales 15 วันที่ผ่านมา

    √91

  • @EdMatthewMorales
    @EdMatthewMorales 15 วันที่ผ่านมา

    √(1001/9

  • @martyn_carter
    @martyn_carter 29 วันที่ผ่านมา

    U

  • @Burning_Wall
    @Burning_Wall 29 วันที่ผ่านมา

    I am so early
    Great Video btw

    • @WrathofMath
      @WrathofMath  28 วันที่ผ่านมา

      Thank you!

  • @stevepryor3147
    @stevepryor3147 28 วันที่ผ่านมา +1

    FAIL!! M=2 is not the only solution. What about when b=0, or m 2 or any form other than (mb,b)? Why did you start with (mb,b), was it just a guess? (a,0) and (a,-a) are also solutions. I can't prove there aren't more. That's why I watch videos like this one. This gets zero on a quiz, part marks at best.

    • @empathogen75
      @empathogen75 28 วันที่ผ่านมา +1

      Oh so are there more than infinity answers?

    • @kyay10
      @kyay10 28 วันที่ผ่านมา +3

      The point was to find how many solutions there are. He proved that there are infinitely many. The fact there's other forms won't change that cardinality

    • @wernerviehhauser94
      @wernerviehhauser94 28 วันที่ผ่านมา +2

      yes, steve, you failed in comprehensivly reading the problem.