MathDB

Problem 1

Part of 1999 Ukraine National Mathematical Olympiad

Problems(4)

syseq, absolute value and floor related (Ukraine 1999 Grade 8 P1)

Source:

5/9/2021
Solve the system of equations 2∣x∣+∣y∣=12|x|+|y|=1, ⌊∣x∣⌋+⌊2∣y∣⌋=2\lfloor|x|\rfloor+\lfloor2|y|\rfloor=2.
absolute valuealgebrasystem of equations
graph of |x^2+xy|≥|x^2-xy| (Ukraine 1999 Grade 9 P1)

Source:

5/10/2021
Describe the region in the coordinate plane defined by ∣x2+xy∣≥∣x2−xy∣|x^2+xy|\ge|x^2-xy|.
graphalgebra
trig equation (Ukraine 1999 Grade 10 P1)

Source:

5/11/2021
Solve the equation sin⁡xsin⁡2xsin⁡3x+cos⁡xcos⁡2xcos⁡3x=1\sin x\sin2x\sin3x+\cos x\cos2x\cos3x=1.
trigonometryalgebra
trig equation, high exponents

Source: Ukraine 1999 Grade 11 P1

5/11/2021
Solve the equation (sin⁡x)1998+(cos⁡x)−1999=(cos⁡x)1998+(sin⁡x)−1999.(\sin x)^{1998}+(\cos x)^{-1999}=(\cos x)^{1998}+(\sin x)^{-1999}.
trigonometryalgebra