Difference between revisions of "2014 USAMO Problems"
(→Problem 2) |
(→Day 1) |
||
Line 2: | Line 2: | ||
===Problem 1=== | ===Problem 1=== | ||
+ | Let <math>a,b,c,d</math> be real numbers such that <math>b-d \ge 5</math> and all zeros <math>x_1, x_2, x_3,</math> and <math>x_4</math> of the polynomial <math>P(x)=x^4+ax^3+bx^2+cx+d</math> are real. Find the smallest value the product <math>(x_1^2+1)(x_2^2+1)(x_3^2+1)(x_4^2+1)</math> can take. | ||
+ | |||
[[2014 USAMO Problems/Problem 1|Solution]] | [[2014 USAMO Problems/Problem 1|Solution]] | ||
===Problem 2=== | ===Problem 2=== | ||
Line 10: | Line 12: | ||
===Problem 3=== | ===Problem 3=== | ||
[[2014 USAMO Problems/Problem 3|Solution]] | [[2014 USAMO Problems/Problem 3|Solution]] | ||
+ | |||
==Day 2== | ==Day 2== | ||
Revision as of 17:38, 29 April 2014
Contents
[hide]Day 1
Problem 1
Let be real numbers such that and all zeros and of the polynomial are real. Find the smallest value the product can take.
Problem 2
Let be the set of integers. Find all functions such that for all with .