{"id":938,"date":"2025-12-08T17:24:14","date_gmt":"2025-12-08T16:24:14","guid":{"rendered":"https:\/\/mymatma.pl\/?p=938"},"modified":"2025-12-08T17:24:18","modified_gmt":"2025-12-08T16:24:18","slug":"zadanie-40","status":"publish","type":"post","link":"https:\/\/mymatma.pl\/?p=938","title":{"rendered":"Zadanie 40"},"content":{"rendered":"\n<p><strong>zadanie 13 \u2013 maj 2021 (1 pkt)<\/strong><\/p>\n\n\n\n<p>Trzywyrazowy ci\u0105g 15,3x,(5\/3) jest geometryczny i wszystkie wyrazy s\u0105 dodatnie. St\u0105d wynika, \u017ce:<\/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=\"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\"><\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\"><\/div>\n<\/div>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\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\"><\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\"><\/div>\n<\/div>\n<\/div>\n<\/div>\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_69e227b0cd65f\">\n        <button class=\"premium-btn-odp\"\n                data-id=\"odp_69e227b0cd65f\"\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 odpowiedz to D.\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_69e227b0cd66c\">\n        <button class=\"premium-btn-wyjasnienie\"\n                data-id=\"wyjasnienie_69e227b0cd66c\"\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\n<div class=\"card\" role=\"article\" style=\"font-family:system-ui,-apple-system,Segoe UI,Roboto,'Helvetica Neue',Arial;line-height:1.5;color:#111;padding:18px;background:#fff;border:1px solid #e2e6ea;border-radius:10px;max-width:760px;margin:16px auto;box-shadow:0 6px 20px rgba(18,38,63,0.06)\"> <p>Dany jest trzywyrazowy ci\u0105g <code>(15, 3x, 5\/3)<\/code>, kt\u00f3ry jest geometryczny i wszystkie wyrazy s\u0105 dodatnie. Obliczamy warto\u015b\u0107 <strong>x<\/strong>.<\/p> <p><strong>Krok 1 \u2014 zapisz r\u00f3wno\u015b\u0107 iloraz\u00f3w:<\/strong><\/p> <p style=\"background:#fbfdff;padding:8px;border-radius:6px;border:1px solid #eef6ff;display:inline-block\"> \\(\\dfrac{3x}{15} = \\dfrac{5\/3}{3x}\\) <\/p> <p><strong>Krok 2 \u2014 pomn\u00f3\u017c krzy\u017cowo:<\/strong><\/p> <p style=\"background:#fbfdff;padding:8px;border-radius:6px;border:1px solid #eef6ff;display:inline-block\"> (3x)\u00b2 = 15 \u00b7 (5\/3) <\/p> <p><strong>Krok 3 \u2014 oblicz lew\u0105 i praw\u0105 stron\u0119:<\/strong><\/p> <p style=\"background:#fbfdff;padding:8px;border-radius:6px;border:1px solid #eef6ff;display:inline-block\"> 9x\u00b2 = 25 \u2192 x\u00b2 = 25 \/ 9 \u2192 x = 5\/3 <\/p> <p><strong>Krok 4 \u2014 uwzgl\u0119dnij warunek dodatnio\u015bci wyraz\u00f3w:<\/strong><\/p> <p style=\"background:#fbfdff;padding:8px;border-radius:6px;border:1px solid #eef6ff;display:inline-block\"> x > 0 \u2192 x = 5\/3 <\/p> <p><strong>Wynik:<\/strong><\/p> <div style=\"margin-top:14px;padding:12px;border-radius:8px;background:#f0faf0;border:1px solid #d8f1d8;color:#066a06;font-weight:600\"> x = <strong>5\/3<\/strong> <\/div> <div style=\"margin-top:14px\"> <span style=\"display:inline-block;padding:8px 10px;border-radius:6px;border:1px solid #ddd;background:#fafafa\">a) 3\/5<\/span> <span style=\"display:inline-block;padding:8px 10px;border-radius:6px;border:1px solid #ddd;background:#fafafa\">b) 4\/5<\/span> <span style=\"display:inline-block;padding:8px 10px;border-radius:6px;border:1px solid #ddd;background:#fafafa\">c) 1<\/span> <span style=\"display:inline-block;padding:8px 10px;border-radius:6px;border:1px solid #1e90ff;background:#e9f4ff;font-weight:600\">d) 5\/3<\/span> <\/div> <\/div>         <\/div>\n    <\/div>\n    \n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>zadanie 13 \u2013 maj 2021 (1 pkt) Trzywyrazowy ci\u0105g 15,3x,(5\/3) jest geometryczny i wszystkie wyrazy s\u0105 dodatnie. St\u0105d wynika, \u017ce:<\/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":[31,117,115,81,83],"tags":[29,116,112],"class_list":["post-938","post","type-post","status-publish","format-standard","hentry","category-ciag-geometryczny","category-maj-2021","category-trzy-kolejne-wyrazy-ciagu","category-zadania-maturalne","category-zadania-tematami","tag-ciag-geometryczny","tag-maj-2021","tag-trzy-kolejne-wyrazy-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 13 \u2013 maj 2021 (1 pkt) Trzywyrazowy ci\u0105g 15,3x,(5\/3) jest geometryczny i wszystkie wyrazy s\u0105 dodatnie. St\u0105d wynika, \u017ce:","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/posts\/938","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=938"}],"version-history":[{"count":1,"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/posts\/938\/revisions"}],"predecessor-version":[{"id":940,"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/posts\/938\/revisions\/940"}],"wp:attachment":[{"href":"https:\/\/mymatma.pl\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=938"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mymatma.pl\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=938"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mymatma.pl\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=938"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}