An Interesting Exponential Equation

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  • Опубликовано: 12 янв 2025

Комментарии • 16

  • @scottleung9587
    @scottleung9587 22 дня назад +2

    Nice!

  • @mystychief
    @mystychief 22 дня назад +2

    A negative x is tricky, that's why there is no graph of the left part, but both of the x-values are valid in this case.

  • @stephenshefsky5201
    @stephenshefsky5201 22 дня назад +1

    Great problem! I was very close to solving it by arranging the equation into log-product form, but I couldn't quite see the path. Then I set y = x^2 - 2x + 1, from which I found the system 0 = x^y - 2x - 1, 0 = x^2 - 2x - y + 1. Subtracting, I found 0 = (x^y - x^2) - (y - 2) which is obviously solvable by y = 2, from which I obtained 0 = x^2 - 2 - 1, and finally x = 1 +/-sqrt(2). Not so elegant, but it worked.

  • @dmtri1974
    @dmtri1974 21 день назад +1

    Nice and clean! Does it have other solutions? exept those 2 and why?

  • @mathpro926
    @mathpro926 21 день назад

    nice solution

  • @hazalouldi7130
    @hazalouldi7130 22 дня назад +2

    multiply both side by lnx and use lambert function.

    • @zawatsky
      @zawatsky 21 день назад

      So uncivilized... 🔫🧔🤏

  • @zawatsky
    @zawatsky 21 день назад +1

    Пробуем решить "в лоб". Предположим, что x-1=√2, тогда х²-2х-1=0. D=4+4=8, x=(2±2√2)/2=1±√2. х=1+√2 подходит.

  • @roberttelarket4934
    @roberttelarket4934 22 дня назад +1

    Houston we have a problem that SyberMath might solve!
    SyberMath we have this problem but thankfully you have the solution!

    • @SyberMath
      @SyberMath  22 дня назад

      @@roberttelarket4934 😍

  • @jesusalej1
    @jesusalej1 22 дня назад +1

    Use an excel graph, it is easier.

  • @Garensonic
    @Garensonic 21 день назад

    Not sure if domain was x >= 0 making the second solution extraneous

  • @dmtri1974
    @dmtri1974 21 день назад

    WolphamAlfa gives also 2 solutions....

  • @rakenzarnsworld2
    @rakenzarnsworld2 22 дня назад +1

    x^2-2x+1=(x-1)^2
    x^{(x-1)^2}=2x+1
    x = 0
    (-1)^4=1, -2+1=-1