MathDB

11.8

Part of III Soros Olympiad 1996 - 97 (Russia)

Problems(2)

integer polynomial with min real root \sqrt2

Source: III Soros Olympiad 1996-97 R1 11.8 https://artofproblemsolving.com/community/c2416727_soros_olympiad_in_mathematics

5/29/2024
Find any polynomial with integer coefficients, the smallest value of which on the entire line is equal to :
a) −2-\sqrt2 b) 2\sqrt2
algebrapolynomial
2x2 trig. system (III Soros Olympiad 1996-97 R3 11.8)

Source:

5/31/2024
Solve the system of equations: 2(3−2cos⁡y)2+2(4−2sin⁡y)2=2(3−x)2+32=(x−2cos⁡y)2+4sin⁡2y 2(3-2\cos y)^2+2(4-2\sin y)^2=2(3-x)^2+32=(x-2\cos y)^2+4\sin^2y
algebratrigonometrysystem of equations