Germany | Can You Solve This??? | A Nice Olympiad Algebra Problem | 99% Failed This...

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  • Опубліковано 21 лис 2024

КОМЕНТАРІ • 7

  • @DanToomey-j8n
    @DanToomey-j8n 12 днів тому

    2 and fun vod is stronger if dogma is constant. R = . Cos² x becomes pi as 2nd function. 3 graphs 1 circa.. 2 π function if x>p0. Point is f§Gunction symbol. 2π² since sinx is nominal part 3 3 becomes answer 3quotient. πr. .. I'm working

  • @pspprabhat
    @pspprabhat 8 днів тому +1

    81^sin^2 x +81^(1-sin^2x)=30
    =>m+81-81/m=30
    =>m^2-30m+81=0
    =>m^2-3m-27m+81=0
    =>m(m-3)-27(m-3)=0
    =>m=3 or 27
    =>3^4sin^2×=3
    &sinx=+_1/2
    Also sinx=+_ _/3/2

  • @satrajitghosh8162
    @satrajitghosh8162 10 днів тому

    writing z = 81 ^ (sin^ 2( x)) one gets
    z + 81/z = 30
    z^2 - 30 z + 81 = 0
    ( z - 27)( z -3) = 0
    This implies z = 27, 3
    = (81) ^ ( 3/4), 81 ^ (1/4)
    Hereby
    81 ^ (sin^ 2( x)) = z
    = (81) ^ ( 3/4), 81 ^ (1/4)
    Hereby
    sin^ 2 ( x) = 3/4, 1/4
    1 - cos (2 x) =2 sin^ 2 ( x) = 3/2, 1/2
    cos (2 x) = - 1/2, 1/2
    cos ^ 2 ( 2 x).= 1/4
    cos (4 x) = 2 cos ^ 2 ( x) - 1 = - 1/2
    Hereby
    4 x = 2 n π + 2 π /3, 2 n π - 2 π /3
    x = (n /2 + 1/6) π, (n /2 - 1/6) π

    • @oahuhawaii2141
      @oahuhawaii2141 2 дні тому

      You missed half the solutions.
      With 4*sin²(x) = 1, 3 , we have:
      sin(x) = ±1/2, ±√3/2
      There are 8 unique solutions between -π and π .