Solution 82: Simple Bashing & Cauchy-Schwarz "Equality"

  • Published on Mar 7, 2019
  • We efficiently solve the trigonometric problem in two different ways, with a subtle use of Cauchy-Schwarz inequality for the second method.
    Congratulations to Rishav Gupta, JIN ZHI PHOONG, Hiren Bavaskar, Serengeti Ghasa, mstmar, adandap, EyyLmaoo, UbuntuLinux, Intergalactic Bajrang dal, and Bintang Alam Semesta W.A.M for successfully solving this math challenge question! Rishav Gupta was the first person to solve the question.
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Comments • 18

  • Super bike And sport
    Super bike And sport 2 months ago

    I love ❤️

  • K Design
    K Design 3 months ago

    can you solve this ? find gamma or beta ; we have only x , y, and alpha

  • Aaron He
    Aaron He 3 months ago +2

    Hi, what is your experience with the art of problem solving volume one book? I am considering to buy it in order to improve my problem solving skills.

    • LetsSolveMathProblems
      LetsSolveMathProblems  3 months ago +2

      AoPS Volume 1, quite simply, is outstanding. It would be one of the first books I would recommend to anyone wishing to build or solidify one's foundation for mathematical problem solving. I personally learned much from Volume 1, as well. =)
      If you have already mastered most of the material in Volume 1, I would strongly recommend checking out Volume 2 (of course!), Paul Zeitz's "Art and Craft of Problem Solving," and Arthur Engel's "Problem Solving Strategies." All three books are superb, although I do warn you that Engel's book requires a certain degree of mathematical maturity.

  • Atharva #breakthrough
    Atharva #breakthrough 3 months ago

    how do u solev it to find this x? value?

  • traso
    traso 3 months ago +3

    I don't take math classes anymore so your videos keep me fresh

  • David Franco
    David Franco 3 months ago

    4:50 :o oh that is the part were I got stuck, I did not recognize the perfect square -.-"

  • Shanmuga Sundaram
    Shanmuga Sundaram 3 months ago

    Did you prove the uniqueness of "x" in the said interval?

    • Marco Dalla Gasperina
      Marco Dalla Gasperina 3 months ago +1

      sinx is monotonic (positive) on [0,pi/2] and so is sin^4(x). cos(x) is monotonic (negative) and so is cos^3(x). Therefore, if they intersect, they can only intersect at one point.

    • Davide
      Davide 3 months ago

      Where would you even need the uniqueness of x?

    • adandap
      adandap 3 months ago

      Not a proof, but Mathematica finds a single root in the interval at ~ 0.835. (In fact it's also a local minimum.) It can also find a closed expression for it, but it's not pretty!
      x = 2 ArcCos[\[Sqrt](5/8 + 1/( 8 Sqrt[3/(19 + (4960 - 96 Sqrt[849])^(1/3) + 2 2^(2/3) (155 + 3 Sqrt[849])^(1/3))]) -
      1/2 \[Sqrt](19/24 - 1/48 (4960 - 96 Sqrt[849])^(1/3) - 1/12 (1/2 (155 + 3 Sqrt[849]))^(1/3) + 9/8 Sqrt[3/(19 + (4960 - 96 Sqrt[849])^(1/3) +
      2 2^(2/3) (155 + 3 Sqrt[849])^(1/3))]))]

  • Pranjal Das
    Pranjal Das 3 months ago +1

    So thanks for the video

  • Pranjal Das
    Pranjal Das 3 months ago +1

    I didn't know the Cauchy's inequality

    • Davide
      Davide 3 months ago

      Pranjal Das bj hahaha

  • Pranjal Das
    Pranjal Das 3 months ago +1

    That's cool

  • adandap
    adandap 3 months ago +4

    I do like me a bit of straightforward bashing! That's my default setting. :)

  • el tapa
    el tapa 3 months ago

    Too Easy for me :p
    Great edition

    HARRIS LAM 3 months ago