{"id":1301,"date":"2025-12-22T13:21:43","date_gmt":"2025-12-22T12:21:43","guid":{"rendered":"http:\/\/mymatma.pl\/?p=1301"},"modified":"2025-12-22T13:21:46","modified_gmt":"2025-12-22T12:21:46","slug":"zadanie-121","status":"publish","type":"post","link":"https:\/\/mymatma.pl\/?p=1301","title":{"rendered":"Zadanie 121"},"content":{"rendered":"\n<p><strong>zadanie 18 \u2013 sierpie\u0144 2023 (zadanie otwarte) (2pkt)<\/strong><\/p>\n\n\n\n<p>Ci\u0105g (3x<sup>2<\/sup>+5x,x<sup>2<\/sup>,20\u2212x<sup>2<\/sup>) jest arytmetyczny. Oblicz x .<\/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_69e22b375f2e2\">\n        <button class=\"premium-btn-odp\"\n                data-id=\"odp_69e22b375f2e2\"\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            \nPrawid\u0142owa odpowied\u017a to x = 1.\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_69e22b375f2f6\">\n        <button class=\"premium-btn-wyjasnienie\"\n                data-id=\"wyjasnienie_69e22b375f2f6\"\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<h3>Wyja\u015bnienie<\/h3>\n\n<p>W zadaniu dany jest trzywyrazowy ci\u0105g:<\/p>\n\n<p style=\"text-align:center;\">\n(3x\u00b2 + 5x, &nbsp; x\u00b2, &nbsp; 20 \u2212 x\u00b2)\n<\/p>\n\n<p>Aby ci\u0105g by\u0142 arytmetyczny, r\u00f3\u017cnica mi\u0119dzy kolejnymi wyrazami musi by\u0107 taka sama. Zapisujemy warunek:<\/p>\n\n<p style=\"text-align:center;\">\nx\u00b2 \u2212 (3x\u00b2 + 5x) = (20 \u2212 x\u00b2) \u2212 x\u00b2\n<\/p>\n\n<h4>1. Upraszczamy lew\u0105 stron\u0119<\/h4>\n\n<p style=\"text-align:center;\">\nx\u00b2 \u2212 3x\u00b2 \u2212 5x = \u22122x\u00b2 \u2212 5x\n<\/p>\n\n<h4>2. Upraszczamy praw\u0105 stron\u0119<\/h4>\n\n<p style=\"text-align:center;\">\n20 \u2212 x\u00b2 \u2212 x\u00b2 = 20 \u2212 2x\u00b2\n<\/p>\n\n<h4>3. Otrzymujemy r\u00f3wnanie<\/h4>\n\n<p style=\"text-align:center;\">\n\u22122x\u00b2 \u2212 5x = 20 \u2212 2x\u00b2\n<\/p>\n\n<p>Dodajemy 2x\u00b2 do obu stron:<\/p>\n\n<p style=\"text-align:center;\">\n\u22125x = 20\n<\/p>\n\n<p>Dzielimy przez \u22125:<\/p>\n\n<p style=\"text-align:center; font-size: 1.2em;\">\n<strong>x = 1<\/strong>\n<\/p>\n\n<h3>Odpowied\u017a:<\/h3>\n<p>Liczba <strong>x<\/strong> jest r\u00f3wna <strong>1<\/strong>.<\/p>\n\n        <\/div>\n    <\/div>\n    \n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>zadanie 18 \u2013 sierpie\u0144 2023 (zadanie otwarte) (2pkt) Ci\u0105g (3&#215;2+5x,x2,20\u2212x2) jest arytmetyczny. Oblicz x .<\/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":[25,34,198,81,83],"tags":[23,199,197],"class_list":["post-1301","post","type-post","status-publish","format-standard","hentry","category-ciag-arytmetyczny","category-sierpien-2023","category-wlasnosci-trzech-kolejnych-wyrazow-ciagu","category-zadania-maturalne","category-zadania-tematami","tag-ciag-arytmetyczny","tag-sierpien-2023","tag-wlasnosci-trzech-kolejnych-wyrazow-ciagu"],"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 18 \u2013 sierpie\u0144 2023 (zadanie otwarte) (2pkt) Ci\u0105g (3x2+5x,x2,20\u2212x2) jest arytmetyczny. Oblicz x .","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/posts\/1301","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=1301"}],"version-history":[{"count":1,"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/posts\/1301\/revisions"}],"predecessor-version":[{"id":1302,"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/posts\/1301\/revisions\/1302"}],"wp:attachment":[{"href":"https:\/\/mymatma.pl\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1301"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mymatma.pl\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1301"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mymatma.pl\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1301"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}