{"id":935,"date":"2025-12-08T17:02:40","date_gmt":"2025-12-08T16:02:40","guid":{"rendered":"https:\/\/mymatma.pl\/?p=935"},"modified":"2025-12-08T17:13:12","modified_gmt":"2025-12-08T16:13:12","slug":"zadanie-39","status":"publish","type":"post","link":"https:\/\/mymatma.pl\/?p=935","title":{"rendered":"Zadanie 39"},"content":{"rendered":"\n<p><strong>zadanie 32 \u2013 czerwiec 2022 (zad. Otwarte) (2 pkt)<\/strong><br>Tr\u00f3jwyrazowy ci\u0105g (x,3x+2,9x+16) jest geometryczny. Oblicz x . Przyznaj sobie samodzielnie punkty, zgodnie z proponowan\u0105 punktacj\u0105 (0 pkt, 1 pkt, 2 pkt)<\/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_69e227409bca9\">\n        <button class=\"premium-btn-odp\"\n                data-id=\"odp_69e227409bca9\"\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_69e227409bcba\">\n        <button class=\"premium-btn-wyjasnienie\"\n                data-id=\"wyjasnienie_69e227409bcba\"\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:1.55;color:#111;padding:20px;background:#fff;border:1px solid #e2e6ea;border-radius:10px;max-width:760px;margin:20px auto;box-shadow:0 6px 20px rgba(18,38,63,0.06)\"> <p>Dany jest trzywyrazowy ci\u0105g <code>(x,\\;3x+2,\\;9x+16)<\/code>, kt\u00f3ry tworzy ci\u0105g geometryczny. Aby obliczy\u0107 warto\u015b\u0107 <strong>x<\/strong>, korzystamy z w\u0142asno\u015bci, \u017ce stosunek kolejnych wyraz\u00f3w jest sta\u0142y.<\/p> <p><strong>Krok 1 \u2014 zapisz r\u00f3wno\u015b\u0107 iloraz\u00f3w:<\/strong><\/p> <p style=\"background:#f7faff;padding:9px 12px;border-radius:6px;border:1px solid #e3edfa;display:inline-block\"> \\(\\displaystyle \\frac{3x+2}{x} = \\frac{9x+16}{3x+2}\\) <\/p> <p><strong>Krok 2 \u2014 wykonaj mno\u017cenie na krzy\u017c:<\/strong><\/p> <p style=\"background:#f7faff;padding:9px 12px;border-radius:6px;border:1px solid #e3edfa;display:inline-block\"> \\((3x+2)^2 = x(9x+16)\\) <\/p> <p><strong>Krok 3 \u2014 rozwi\u0144 nawiasy i uporz\u0105dkuj r\u00f3wnanie:<\/strong><\/p> <p style=\"background:#f7faff;padding:9px 12px;border-radius:6px;border:1px solid #e3edfa;display:inline-block\"> \\(9x^2 + 12x + 4 = 9x^2 + 16x\\) <\/p> <p><strong>Krok 4 \u2014 skr\u00f3\u0107 r\u00f3wnanie i oblicz x:<\/strong><\/p> <p style=\"background:#f7faff;padding:9px 12px;border-radius:6px;border:1px solid #e3edfa;display:inline-block\"> \\(12x + 4 = 16x\\)<br> \\(4 = 4x\\)<br> \\(x = 1\\) <\/p> <p><strong>Wynik:<\/strong><\/p> <div style=\"margin-top:14px;padding:14px;border-radius:8px;background:#f0faf0;border:1px solid #d8f1d8;color:#066a06;font-weight:600;font-size:17px\"> \\(x = \\mathbf{1}\\) <\/div> <div style=\"margin-top:16px\"> <p><strong>Punktacja (przyznaj sobie samodzielnie):<\/strong><\/p> <ul style=\"padding-left:18px;margin:8px 0\"> <li><strong>2 pkt<\/strong> \u2014 pe\u0142ne i poprawne rozwi\u0105zanie z r\u00f3wnaniem iloraz\u00f3w i przekszta\u0142ceniami.<\/li> <li><strong>1 pkt<\/strong> \u2014 cz\u0119\u015bciowe rozwi\u0105zanie lub brak jednego kroku.<\/li> <li><strong>0 pkt<\/strong> \u2014 b\u0142\u0119dne obliczenia lub brak poprawnej metody.<\/li> <\/ul> <\/div> <\/div>         <\/div>\n    <\/div>\n    \n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>zadanie 32 \u2013 czerwiec 2022 (zad. Otwarte) (2 pkt)Tr\u00f3jwyrazowy ci\u0105g (x,3x+2,9x+16) jest geometryczny. Oblicz x . Przyznaj sobie samodzielnie punkty, zgodnie z proponowan\u0105 punktacj\u0105 (0 pkt, 1 pkt, 2 pkt)<\/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":[31,114,115,81,83],"tags":[29,113,112],"class_list":["post-935","post","type-post","status-publish","format-standard","hentry","category-ciag-geometryczny","category-czerwiec-2022","category-trzy-kolejne-wyrazy-ciagu","category-zadania-maturalne","category-zadania-tematami","tag-ciag-geometryczny","tag-czerwiec-2022","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 32 \u2013 czerwiec 2022 (zad. Otwarte) (2 pkt)Tr\u00f3jwyrazowy ci\u0105g (x,3x+2,9x+16) jest geometryczny. Oblicz x . Przyznaj sobie samodzielnie punkty, zgodnie z proponowan\u0105 punktacj\u0105 (0 pkt, 1 pkt, 2 pkt)","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/posts\/935","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=935"}],"version-history":[{"count":2,"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/posts\/935\/revisions"}],"predecessor-version":[{"id":939,"href":"https:\/\/mymatma.pl\/index.php?rest_route=\/wp\/v2\/posts\/935\/revisions\/939"}],"wp:attachment":[{"href":"https:\/\/mymatma.pl\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=935"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mymatma.pl\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=935"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mymatma.pl\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=935"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}