Math Olympiad | A Nice Exponential Problem | 90% Failed to solve !

2024 ж. 10 Ақп.
12 810 Рет қаралды

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Пікірлер
  • Muy buen ejercicio, lo he disfrutado muchísimo. Gracias profesor, un saludo desde Lima, Perú

    @daniellopez3124@daniellopez31242 ай бұрын
  • Excelente trabajo. Un abrazo. Saludos.

    @johnnyfarfan1723@johnnyfarfan17232 ай бұрын
    • Thank you ⚘️

      @vijaymaths5483@vijaymaths54832 ай бұрын
  • (7:35) What you do at this point is an auguration of the solution. This has only a use in one (of endlessly many) cases - if the value of x IS IN FACT 2. BUT: IF you DO augur the end result (in that you manipulate expressions in a way that has no allowance except the one and only case where the augurated result does apply), then you could have simplified the whole matter drastically, in that you could have tested the augurated result in the original expression. In fact, first i have solved this case in that way - trying to imagine an approximate value (which is trivial at first glance "about 2"), then testing how far away from the destination that would be - only to see that it is actually a solution. And since the expressions sqrt(2)+1 and sqrt(2)-1 are invers to each other, it was as well trivial to deduce that a second solution must exist with negated value. To solve that problem in a generalized way, you have to take logarithms. Let's say the LHS should equal an arbitrary K. Then you get the t in your midway approach as t = k/2 +- sqrt( k^2 / 4 - 1 ) Then the generalized solution is log( t ) / log( sqrt(2)-1 ) ...for t1 and t2.

    @WhiteGandalfs@WhiteGandalfs3 ай бұрын
    • Got it... Thank you for your feedback master👍👏

      @vijaymaths5483@vijaymaths54833 ай бұрын
    • But all the point with this problem is of being a special case and not a general one. Moreover, you don’t have to augur the end result from the start, but just to find out that the intermediate result (3±2√2) equals to (√2+1) raised to an integer power (±2) .

      @shmuelzehavi4940@shmuelzehavi4940Ай бұрын
  • Excelente didática professor.

    @antonio9633@antonio96333 ай бұрын
    • Thank you 🙏😊

      @vijaymaths5483@vijaymaths54833 ай бұрын
  • At minute 6:39 you have 6 sqrt2 divided by 2. It should be 3sqrt2 for the second half of the sum, not 2sqrt2. Hope this helps.

    @LeakyFaucett@LeakyFaucett2 ай бұрын
    • 4 square root 2 divided by 2 means 2 square 2 ( square root 32 = 4 square root 2 ) Please recheck once again that part 🎉

      @prabhushettysangame6601@prabhushettysangame66012 ай бұрын
    • Ok hi hai, aur ek baar check kijiye

      @vijaymaths5483@vijaymaths54832 ай бұрын
  • Gracias por compartir el vídeo y la solución del ejercicio. Saludos desde Chiclayo Norte del Perú.

    @juliovasquezdiaz2432@juliovasquezdiaz24322 ай бұрын
    • Thanks too for your valuable feedback 🖍

      @vijaymaths5483@vijaymaths54832 ай бұрын
  • It can be solved by putting x=0,1 or 2. Then solution will be x=2. The short method.

    @neerarajpoot8409@neerarajpoot84093 ай бұрын
    • Thank you for your feedback!! 😊

      @vijaymaths5483@vijaymaths54833 ай бұрын
  • Thanks too much sir, I'm following yourself by that excellent nice and beautiful problems, thanks again.

    @ezzatabdo5027@ezzatabdo50273 ай бұрын
    • Thanks a lot 🎈

      @vijaymaths5483@vijaymaths54833 ай бұрын
  • SENSACIONAL!!

    @Danieswors@Danieswors3 ай бұрын
    • Thank you 🙏

      @vijaymaths5483@vijaymaths54833 ай бұрын
  • Guess one solution x=2. a^x is strictly monotonically increasing for a>0, so x=2 is the only real solution. Finish.

    @jaju2178@jaju21782 ай бұрын
  • Thank you for clear explaining

    @yasharhashimov9063@yasharhashimov90633 ай бұрын
    • Welcome 😊

      @vijaymaths5483@vijaymaths54833 ай бұрын
  • Nicely explained!

    @ncslovers3429@ncslovers34293 ай бұрын
    • Thanks!

      @vijaymaths5483@vijaymaths54833 ай бұрын
  • X=2

    @user-nd7th3hy4l@user-nd7th3hy4l2 ай бұрын
  • Great.

    @adroaldoferreira978@adroaldoferreira9783 ай бұрын
    • Lot of thanks

      @vijaymaths5483@vijaymaths54833 ай бұрын
  • (x+2x-3)

    @user-ri6rn7ti5h@user-ri6rn7ti5h3 ай бұрын
  • Этот пример уже был решен другим автором.

    @user-ee7nw2rx9s@user-ee7nw2rx9s2 ай бұрын
  • Great explanation 👍

    @sumit-mn6ys@sumit-mn6ys3 ай бұрын
    • Glad you liked it

      @vijaymaths5483@vijaymaths54833 ай бұрын
  • 👏👏👏

    @superiorlyrics8326@superiorlyrics83263 ай бұрын
    • 🙏🙏

      @vijaymaths5483@vijaymaths54833 ай бұрын
  • Squiroot

    @wRAAh@wRAAh2 ай бұрын
  • (x+3x-3)

    @user-ri6rn7ti5h@user-ri6rn7ti5h3 ай бұрын
    • 🤨

      @vijaymaths5483@vijaymaths54833 ай бұрын
  • asnwer=3 isit

    @comdo777@comdo7773 ай бұрын
    • No! Answer is 2 & -2...Thanks for watching 😊

      @vijaymaths5483@vijaymaths54833 ай бұрын
  • 2

    @jaggisaram4914@jaggisaram49143 ай бұрын
    • Correct.. thanks for watching 🙂

      @vijaymaths5483@vijaymaths54833 ай бұрын
  • молодец, садись, 4ре)

    @klopklop6055@klopklop60552 ай бұрын
  • X=2

    @AvinashKumar-yz2tf@AvinashKumar-yz2tfАй бұрын
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