MathDB

3

Part of 2015 Czech-Polish-Slovak Junior Match

Problems(2)

x^2 + y^2 <= 2 => xy + 3 >= 2x + 2y

Source: Czech-Polish-Slovak Junior Match 2015, Individual p3 CPSJ

3/15/2020
Real numbers x,yx, y satisfy the inequality x2+y2≤2x^2 + y^2 \le 2. Orove that xy+3≥2x+2yxy + 3 \ge 2x + 2y
inequalitiesalgebra
|BE - CE| < AD \sqrt3 when AB = BC= CD and AD \perp BC

Source: Czech-Polish-Slovak Junior Match 2015, Team p3 CPSJ

3/19/2020
Different points AA and DD are on the same side of the line BCBC, with ∣AB∣=∣BC∣=∣CD∣|AB| = | BC|= |CD| and lines ADAD and BCBC are perpendicular. Let EE be the intersection point of lines ADAD and BCBC. Prove that ∣∣BE∣−∣CE∣∣<∣AD∣3||BE| - |CE|| < |AD| \sqrt3
geometrygeometric inequalityequal segmentsperpendicular