MathDB

11.1

Part of V Soros Olympiad 1998 - 99 (Russia)

Problems(3)

x^5 + ... + (x + 1998)^5 = 0 (V Soros Olympiad 1998-99 Round 1 11.)

Source:

5/25/2024
Solve the equation x5+(x+1)5+(x+2)5+...+(x+1998)5=0.x^5 + (x + 1)^5 + (x + 2)^5 + ... + (x + 1998)^5 = 0.
algebra
9 sin x +40 cos x >=41 (V Soros Olympiad 1998-99 Round 2 11.1)

Source:

5/25/2024
Find all xx for which the inequality holds 9sin⁡x+40cos⁡x≥41.9 \sin x +40 \cos x \ge 41.
algebrainequalitiestrigonometry
sin(2log_2 x)+tg(3log_2 x)=sin6+tg9 (V Soros Olympiad 1998-99 Round 3 11.1)

Source:

5/26/2024
Find at least one root of the equationsin⁡(2log⁡2x)+tg(3log⁡2x)=sin⁡6+tg9\sin(2 \log_2 x) + tg(3\log_2 x) = \sin6+tg9less than 0.010.01.
algebratrigonometrylogarithms