{"id":1576,"date":"2025-12-31T12:38:08","date_gmt":"2025-12-31T11:38:08","guid":{"rendered":"http:\/\/mymatma.pl\/?p=1576"},"modified":"2025-12-31T12:38:11","modified_gmt":"2025-12-31T11:38:11","slug":"zadanie-152","status":"publish","type":"post","link":"https:\/\/mymatma.pl\/?p=1576","title":{"rendered":"Zadanie 152"},"content":{"rendered":"\n<p><strong>zadanie 5 &#8211; informator CKE (zadanie otwarte) (2pkt)<\/strong><\/p>\n\n\n\n<p>Wyka\u017c, \u017ce dla ka\u017cdej liczby naturalnej n\u22651 liczba n(n<sup>2<\/sup>+3n+2) jest podzielna przez 6.<\/p>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n    <div class=\"premium-wrapper-odp\" id=\"odp_69e22b3aee747\">\n        <button class=\"premium-btn-odp\"\n                data-id=\"odp_69e22b3aee747\"\n                style=\"margin-top:10px; padding:12px 20px; background:#28a745; color:#fff; border-radius:25px; border:none; cursor:pointer; font-weight:bold;\">\n            Poka\u017c odpowied\u017a\n        <\/button>\n\n        <div class=\"premium-content-odp\" style=\"display:none; padding:15px; border:1px solid #28a745; margin-top:10px; background:#e6ffe6; border-radius:25px;\">\n            \n<p>Iloczyn trzech kolejnych liczb n(n+1)(n+2) zawsze zawiera liczb\u0119 parzyst\u0105 i liczb\u0119 podzieln\u0105 przez 3, wi\u0119c ca\u0142o\u015b\u0107 jest podzielna przez 6.<\/p>\n        <\/div>\n    <\/div>\n    \n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n    <div class=\"premium-wrapper-wyjasnienie\" id=\"wyjasnienie_69e22b3aee753\">\n        <button class=\"premium-btn-wyjasnienie\"\n                data-id=\"wyjasnienie_69e22b3aee753\"\n                style=\"margin-top:10px; padding:12px 20px; background:#28a745; color:#fff; border-radius:25px; border:none; cursor:pointer; font-weight:bold;\">\n            Poka\u017c wyja\u015bnienie\n        <\/button>\n\n        <div class=\"premium-content-wyjasnienie\" style=\"display:none; padding:15px; border:1px solid #28a745; margin-top:10px; background:#e6ffe6; border-radius:25px;\">\n            \n<h2>Wyja\u015bnienie<\/h2>\n\n<p>Chcemy wykaza\u0107, \u017ce dla ka\u017cdej liczby naturalnej <strong>n \u2265 1<\/strong> wyra\u017cenie<\/p>\n\n<p><code>n(n\u00b2 + 3n + 2)<\/code><\/p>\n\n<p>jest podzielne przez <strong>6<\/strong>, czyli jednocze\u015bnie przez <strong>2<\/strong> i przez <strong>3<\/strong>.<\/p>\n\n<h3>Krok 1: Roz\u0142\u00f3\u017cmy wyra\u017cenie na czynniki<\/h3>\n\n<p>\nn(n\u00b2 + 3n + 2) = n(n + 1)(n + 2)\n<\/p>\n\n<p>Otrzymujemy iloczyn trzech kolejnych liczb naturalnych.<\/p>\n\n<h3>Krok 2: Podzielno\u015b\u0107 przez 2<\/h3>\n\n<p>W\u015br\u00f3d trzech kolejnych liczb zawsze jedna jest parzysta, wi\u0119c ca\u0142y iloczyn jest podzielny przez <strong>2<\/strong>.<\/p>\n\n<h3>Krok 3: Podzielno\u015b\u0107 przez 3<\/h3>\n\n<p>W\u015br\u00f3d trzech kolejnych liczb zawsze jedna jest podzielna przez <strong>3<\/strong>, wi\u0119c ca\u0142y iloczyn jest podzielny przez <strong>3<\/strong>.<\/p>\n\n<h3>Krok 4: Wniosek<\/h3>\n\n<p>Skoro wyra\u017cenie jest jednocze\u015bnie podzielne przez 2 i przez 3, to musi by\u0107 podzielne przez <strong>6<\/strong>.<\/p>\n\n<p><strong>Zatem dla ka\u017cdego n \u2265 1 liczba n(n\u00b2 + 3n + 2) jest podzielna przez 6.<\/strong><\/p>\n\n        <\/div>\n    <\/div>\n    \n<\/div>\n<\/div>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>zadanie 5 &#8211; informator CKE (zadanie otwarte) (2pkt) Wyka\u017c, \u017ce dla ka\u017cdej liczby naturalnej n\u22651 liczba n(n2+3n+2) jest podzielna przez 6.<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"saved_in_kubio":false,"_uag_custom_page_level_css":"","_themeisle_gutenberg_block_has_review":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[25,130,204,81,83],"tags":[23,129,205],"class_list":["post-1576","post","type-post","status-publish","format-standard","hentry","category-ciag-arytmetyczny","category-informator-cke","category-rozne","category-zadania-maturalne","category-zadania-tematami","tag-ciag-arytmetyczny","tag-informator-cke","tag-rozne"],"jetpack_featured_media_url":"","uagb_featured_image_src":{"full":false,"thumbnail":false,"medium":false,"medium_large":false,"large":false,"1536x1536":false,"2048x2048":false,"kubio-fullhd":false,"woocommerce_thumbnail":false,"woocommerce_single":false,"woocommerce_gallery_thumbnail":false},"uagb_author_info":{"display_name":"adminmymatma","author_link":"https:\/\/mymatma.pl\/?author=1"},"uagb_comment_info":0,"uagb_excerpt":"zadanie 5 &#8211; informator CKE (zadanie otwarte) (2pkt) Wyka\u017c, \u017ce dla ka\u017cdej liczby naturalnej n\u22651 liczba n(n2+3n+2) jest podzielna przez 6.","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/posts\/1576","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mymatma.pl\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1576"}],"version-history":[{"count":1,"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/posts\/1576\/revisions"}],"predecessor-version":[{"id":1584,"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/posts\/1576\/revisions\/1584"}],"wp:attachment":[{"href":"https:\/\/mymatma.pl\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1576"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mymatma.pl\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1576"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mymatma.pl\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1576"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}