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131	EGMO 2016, Day 1 – Solutions Problem 1. Let n be an odd positive integer, and let x1 , x2 , . . ., xn be non-negative real numbers. Show that min (x2i + x2i+1 ) ≤ max (2xj xj+1 ), j=1,...,n Add to Reading List Source URL: www.egmo.org Language: English - Date: 2016-05-08 06:06:56
132	Kotitehtävät, joulukuu 2011 Helpompi sarja 1. Ratkaise yhtälöryhmä x2 + y 2 = 2z y 2 + z 2 = 2x z 2 + x2 = 2y Add to Reading List Source URL: matematiikkakilpailut.fi Language: Finnish - Date: 2016-06-12 06:38:25
133	Language: Ukrainian Day: 1 Вiвторок, 12 квiтня, 2016 р. Задача 1. Нехай n – непарне натуральне число i x1 , x2 , ..., xn – невiд’ємнi дiйснi числа. До Add to Reading List Source URL: www.egmo.org Language: Ukrainian - Date: 2016-04-12 06:30:27
134	Language: Albanian Day: 1 E marte, 12 prill, 2016 Problem 1. Le të jetë n një numër natyror tek dhe x1 , x2 , … , xn numra realë jo negativë. Tregoni që Add to Reading List Source URL: www.egmo.org Language: Albanian - Date: 2016-04-16 13:57:59
135	Language: Bosnian Day: 1 Utorak, 12. aprilZadatak 1. Neka je n neparan prirodan broj, i neka su x1 , x2 , . . ., xn nenegativni realni brojevi. Dokazati da vrijedi Add to Reading List Source URL: www.egmo.org Language: Croatian - Date: 2016-04-12 06:30:27
136	Language: Bulgarian Day: 2 Сряда, 13 Април, 2016 Задача 4. Окръжностите ω1 и ω2 имат равни радиуси и се пресичат в точки X1 и X2 . Окръжност ω с Add to Reading List Source URL: www.egmo.org Language: Bulgarian - Date: 2016-04-13 06:30:12
137	Proving Points are the Vertices of a Right Triangle Given the points (13, -1), (-9, 3), and (-3, -9), prove that the points are that of a Right Triangle. Using the distance formula d  ( x2  x1 )2  ( y 2  y1 ) Add to Reading List Source URL: sradai.tripod.com Language: English - Date: 2015-12-01 16:04:48
138	Language: Finnish Day: 2 Keskiviikkona 13. huhtikuuta 2016 Tehtävä 4. Kaksi samansäteistä ympyrää ω1 ja ω2 leikkaavat toisensa kahdessa eri pisteessä X1 ja X2 . Tarkastellaan ympyrää ω, joka sivuaa ympyrää Add to Reading List Source URL: www.egmo.org Language: Finnish - Date: 2016-04-13 06:30:12
139	Language: Albanian Day: 1 E marte, 12 prill, 2016 Problem 1. Le të jetë n një numër natyror tek dhe x1 , x2 , … , xn numra realë jo negativë. Tregoni që Add to Reading List Source URL: www.egmo.org Language: Albanian - Date: 2016-04-16 13:57:59
140	Kesän valmennustehtäväsarja Ratkaisuja Helpompia tehtäviä 1. Olkoot yhtälön x2 + (p2 + 1)x + p = 2 ratkaisut x1 ja x2 , ja olkoot ne nollasta poikkeavia sekä erisuuria. Määritä kaikki parametrin p arvot, joill Add to Reading List Source URL: matematiikkakilpailut.fi Language: Finnish - Date: 2016-06-12 06:38:25

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