{"id":"informator-maturalny-matematyka-2010/zad/54","paper_id":"informator-maturalny-matematyka-2010","number":"54","points":2,"ptype":"open","subject":"matematyka","category":"informator-maturalny","year":2010,"month":null,"level":null,"text":"Zadanie 54. (2 pkt)\nRozwiąż równanie\n0\n3\n6\n2\n2\n3\nx\nx\nx","answer":null,"answer_text":null,"solution":"2x^3-x^2-6x+3=0. Grupujemy: x^2(2x-1) - 3(2x-1) = 0, czyli (2x-1)(x^2-3)=0.\nStąd x=1/2 lub x^2=3, czyli x=sqrt(3) lub x=-sqrt(3).\nOdpowiedź: x=1/2, x=sqrt(3) lub x=-sqrt(3).","image":"img/informator-maturalny-matematyka-2010/zad-54.webp","solution_image":null,"topics":null,"page_from":84,"source":"ai","answer_source":null,"answer_text_source":null,"solution_source":"ai","text_source":"ocr","source_label":"Matematyka · Informator maturalny · 2010","subject_label":"Matematyka","category_label":"Informator maturalny","text_html":"<p>Zadanie 54. (2 pkt)<br>Rozwiąż równanie<br>0<br>3<br>6<br>2<br>2<br>3<br>x<br>x<br>x</p>","solutions":[{"source":"ai","label":"AI","kind":"text","html":"<p>2x^3-x^2-6x+3=0. Grupujemy: x^2(2x-1) - 3(2x-1) = 0, czyli (2x-1)(x^2-3)=0.<br>Stąd x=1/2 lub x^2=3, czyli x=sqrt(3) lub x=-sqrt(3).<br>Odpowiedź: x=1/2, x=sqrt(3) lub x=-sqrt(3).</p>"}]}