{"id":"site-2669/zad/3183","paper_id":"site-2669","number":"3183","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"podstawowa","text":"Udowodnij, że jeśli a) x, y są liczbami rzeczywistymi, to x^2+y^2 >= 2xy, b) x, y, z są liczbami rzeczywistymi takimi, że x+y+z=1, to x^2+y^2+z^2 >= 1/3","answer":null,"answer_text":null,"solution":null,"image":"img/site/2669/zad-3183.svg","solution_image":"img/site/2669/rozw-3183.svg","topics":null,"page_from":null,"source":"site","answer_source":null,"answer_text_source":null,"solution_source":null,"text_source":"site","source_label":"Matematyka · Zbiory zadań (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań","text_html":"<p>Udowodnij, że jeśli a) x, y są liczbami rzeczywistymi, to x^2+y^2 &gt;= 2xy, b) x, y, z są liczbami rzeczywistymi takimi, że x+y+z=1, to x^2+y^2+z^2 &gt;= 1/3</p>","solutions":[{"source":"site","label":"matematykaszkolna.pl","kind":"image","image":"/img/site/2669/rozw-3183.svg"}]}