MathDB

11.3

Part of IV Soros Olympiad 1997 - 98 (Russia)

Problems(3)

\sqrt{(x-2)^2(x-x^2)}<.. (IV Soros Olympiad 1997-98 Correspondence 11.3)

Source:

6/1/2024
Solve the inequality (x−2)2(x−x2)<4x−1−(x2−3x)2\sqrt{(x-2)^2(x-x^2)}<\sqrt{4x-1-(x^2-3x)^2}
algebrainequalitiesRadicals
sinx cos^2 y +sin y cos^2 x =0 (IV Soros Olympiad 1997-98 R2 11.3)

Source:

6/1/2024
Draw on the coordinate plane the set of points whose coordinates satisfy the equation sin⁡xcos⁡2y+sin⁡ycos⁡2x=0\sin x \cos^2 y +\sin y \cos^2 x =0
trigonometryanalytic geometry
| ... |||x^2-x| -1|-1 |...-1|=x^2-2x-14 (IV Soros Olympiad 1997-98 R3 11.3)

Source:

6/2/2024
Solve the equation ∣...∣∣∣x2−x∣−1∣−1∣...−1∣=x2−2x−14.\left| ... \left|\left||x^2-x| -1\right|-1 \right|...-1\right|=x^2-2x-14. (There are 1111 units on the left side.)
algebra