A Very Nice Math Olympiad Problem | Solve the Radical Equation| Algebra

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  • Опубліковано 25 січ 2025

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  • @touratiaziz5059
    @touratiaziz5059 10 днів тому

    🎉

  • @briancurtis466
    @briancurtis466 Місяць тому +1

    The thing that really bothers me is when a teacher says, "Our next step is such and such" but doesn't explain how we come to know that. 6:25 - I know that you know to square both sides, but how was I going to know that? Not a rhetorical question. I want to know how to deduce that I need to square both sides.

  • @kajalbanerjee8220
    @kajalbanerjee8220 Місяць тому

    Root 3/2

  • @raghvendrasingh1289
    @raghvendrasingh1289 Місяць тому +1

    👍
    x = (√3+1)/2
    we know that
    (a+b)^3 = a^3+3(a^2)b+3 a(b^2)+b^3
    x^3 = (3√3+3(3)+3√3+1)/8
    X^3 = (3√3+5)/4
    x^9 = { 27(3√3)+3(27)(5)+3(3√3)(25)+125 } /64
    x^9 = (530+306√3)/64
    x^9 = (265+153√3)/32

    • @에스피-z2g
      @에스피-z2g Місяць тому +1

      P=given formula
      P=x^9
      x=(rt3+1)/2
      2x=rt3+1
      4x^2=4+2rt3
      2x^2=2+rt3
      4x^4=7+4rt3
      16x^8=97+56rt3
      32x^9=97rt3+168
      +97+56rt3=
      265+153rt3
      x^9=(264+153rt3)/32

  • @HansDockhorn-eu7qz
    @HansDockhorn-eu7qz Місяць тому

    This is not an equation, it’s an expression.

  • @Rev03FFL
    @Rev03FFL Місяць тому +1

    I'm not sure the final answer (153*sqr(3)+265)/32 is any simpler than what we started with [(sqr(3)+1)/2]^9. ;)

    • @Twodoor1
      @Twodoor1 Місяць тому +1

      It is cuz no irrational on denominator and bracket expanded out

  • @ирина-ф2м6г
    @ирина-ф2м6г Місяць тому

    I solved this problem
    without x, using by pairs the formula of the square of the sum.