American | Junior Math Olympiad | A Nice Algebra Problem | Simplify?

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  • Опубліковано 17 жов 2024

КОМЕНТАРІ • 10

  • @alexanderbrinkley4332
    @alexanderbrinkley4332 2 місяці тому +6

    In the time you have written all the manipulations, you could have easily raised 5 to the 11th power and subtracted 9.

    • @Mal1234567
      @Mal1234567 2 місяці тому

      It said to simplify, not solve, without using a calculator.

  • @VictorPensioner
    @VictorPensioner 2 місяці тому +4

    5^11 = (5^11 * 2^11) / 2^11 = 10^11 / 2^11 = 1 000 000 000 00 / (2 * 1024) = 1 000 000 000 00 / 2048 = 48828125
    5^11 - 3^2 = 48828125 - 9 = 48828116

  • @walterwen2975
    @walterwen2975 2 місяці тому +3

    Junior Math Olympiad: 5¹¹ - 3² = ?
    5¹¹ = (5³)(5²)⁴ = 125[(25)⁴] = 125[(25²)²] = 125(625²)
    625² = (600 + 25)² = 600² + 2(600)(25) + 25² = 360625 + 30000 = 390600 + 25
    125(625²) = (100 + 25)(390600 + 25) = 39060000 + 25(390600) + 2500 + 625
    = 39063125 + (20 + 5)(390600) = 39063125 + 7812000 + 1953000 = 48828125
    5¹¹ - 3² = 48828125 - 9 = 48828116

  • @henridegueldre1202
    @henridegueldre1202 2 місяці тому +1

    Are you sure that it wasn't be best to calcultate 5^11 directly ? 10 minutes to manipulate, without strong idea, 5^11-3^2...

    • @Mal1234567
      @Mal1234567 2 місяці тому

      It said to simplify, not solve.

  • @Mal1234567
    @Mal1234567 2 місяці тому

    {9 = 5 + 4}
    What is this, some rare theorem we've never heard of before? LOL.

  • @Mal1234567
    @Mal1234567 2 місяці тому

    Much of this solution requires a calculator unless you have the solution to 31 x 31 memorized, and other things like that.

  • @hn4806
    @hn4806 2 місяці тому +2

    Your approach does not seem any better than direct calculation. 5**11=[(5**3)**3]x25=125**3x25 ~ 4 multiplication
    knowing 5**3=125 and 5**2=25. Much smaller # of multiplications with this no-brainer approach.

    • @Mal1234567
      @Mal1234567 2 місяці тому

      It said to simplify, not solve, without a calculator.