5:[["$","div",null,{"className":"crumbs","children":[["$","span",null,{"children":["$","a",null,{"href":"/","children":"Главная"}]}],["$","span",null,{"children":["$","a",null,{"href":"/gdz","children":"ГДЗ"}]}],["$","span",null,{"children":["$","a",null,{"href":"/gdz/algebra/8-klass/makarychev","children":["Алгебра"," ",8," класс ","Макарычев"]}]}],["$","span",null,{"children":["Номер ","1011"]}]]}],["$","h1",null,{"children":["Номер 1011"," — ГДЗ ","алгебра"," ",8," класс ","Макарычев"]}],[["$","section","15003",{"children":[false,["$","div",null,{"className":"sheet-card statement","children":[["$","p",null,{"children":["$","b",null,{"children":["№ 1011","."]}]}],["$","div",null,{"dangerouslySetInnerHTML":{"__html":"

Докажите, что если x + y + z = 1, то

\n$$\\sqrt{4x + 1}$$ + $$\\sqrt{4y + 1}$$ + $$\\sqrt{4z + 1}$$ ≤ 5\n

"}}]]}],["$","div",null,{"className":"notice","children":["Разбор этого задания готовится. Пока можно ",["$","a",null,{"href":"/reshit","children":"решить его по фото"}]," — ИИ объяснит по шагам."]}]]}]],["$","p",null,{"children":[["$","a",null,{"href":"/gdz/algebra/8-klass/makarychev/nomer-1010","children":["← ","Номер 1010"]}]," · ",["$","a",null,{"href":"/gdz/algebra/8-klass/makarychev/nomer-1012","children":["Номер 1012"," →"]}]," · ",["$","a",null,{"href":"/gdz/algebra/8-klass/makarychev","children":"Все номера"}]]}],["$","script",null,{"type":"application/ld+json","dangerouslySetInnerHTML":{"__html":"[{\"@context\":\"https://schema.org\",\"@type\":\"Question\",\"name\":\"Алгебра 8 класс Макарычев, номер 1011\",\"text\":\"Докажите, что если x + y + z = 1, то $$\\\\sqrt{4x + 1}$$ + $$\\\\sqrt{4y + 1}$$ + $$\\\\sqrt{4z + 1}$$ ≤ 5\",\"answerCount\":1,\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"Ответ: Доказано по неравенству Коши-Буняковского: (√(4x + 1) + √(4y + 1) + √(4z + 1))² ≤ 3(4(x + y + z) + 3) = 3 · 7 = 21, откуда сумма ≤ √21 ≈ 4,58 < 5.\"}},{\"@context\":\"https://schema.org\",\"@type\":\"BreadcrumbList\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Главная\",\"item\":\"https://reshay.ai/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"ГДЗ\",\"item\":\"https://reshay.ai/gdz\"},{\"@type\":\"ListItem\",\"position\":3,\"name\":\"Алгебра 8 класс Макарычев\",\"item\":\"https://reshay.ai/gdz/algebra/8-klass/makarychev\"},{\"@type\":\"ListItem\",\"position\":4,\"name\":\"Номер 1011\"}]}]"}}]]

Номер 1011 — ГДЗ алгебра 8 класс Макарычев