MathDB

11.7

Part of I Soros Olympiad 1994-95 (Rus + Ukr)

Problems(2)

tangent twice at y = x^4-x^2 + x (I Soros Olympiad 1994-95 R1 11.7)

Source:

8/1/2021
Write the equation of the line tangent to the graph of the function y=x4−x2+xy = x^4-x^2 + x to at least at two points.
analysisalgebraTangent Line
sin^3 x+sin^4 y=1, cos^4 x+cos^5 y =1 (I Soros Olympiad 1994-99 Round 2 11.7)

Source:

5/26/2024
Solve the system of equations {sin⁡3x+sin⁡4y=1cos⁡4x+cos⁡5y=1\begin{cases} \sin^3 x+\sin^4 y=1 \\ \cos^4 x+\cos^5 y =1\end{cases}
algebrasystem of equationstrigonometry