[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-69232-es":3,"doc-seo-69232-110":30,"detail-sidebar-cat-0-es-110":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":21,"is_downloadable":21,"audit_status":21,"page_count":22,"language":23,"language_code":24,"site_id":25,"html_lang":24,"table_of_contents":26,"faqs":27,"seo_title":28,"seo_description":14,"update_tm":29,"read_time":20},69232,2336475104957,"Seraphina","https://ap-avatar.wpscdn.com/avatar/22000c4c6bd8a5076e1?x-image-process=image/resize,m_fixed,w_180,h_180&k=1786593998035447633",38,"Examen","Ecuaciones Racionales Irracionales y Bicuadradas y Bícubicas","Guía de matemáticas con ejercicios y resultados para resolver ecuaciones de distintos tipos: racionales, irracionales y de mayor grado bicuadradas y bícubicas. Presenta una lista numerada de ecuaciones, seguida por un bloque de “Soluciones” donde se indican los valores de x correspondientes a cada ejercicio. El material enfatiza la práctica de manipulación algebraica y la obtención de raíces para ecuaciones con expresiones polinómicas y radicales.","I. E.S. Arroyo de la Miel Dpto de Matemáticas  \nECUACIONES RACIONALES  \n1. 3 = x - 1 2. x + 2 - x + 3 = 2x + 2  \nx +1 x-1 x-1 x +1 x2-1  \n3. 2 + 3x-3 = 2 + 7 x +1 x2-1 x-1 x +1  \n4. 5 - 3 - 2 3 = 5 5. 15 - 12x2 +6 = 18  \nx-1 x + 4 x + 3x-4 x-1 x-2 x -4 x + 2  \nx +1  \n1 +  \n6. x 1-a + x  a = x2 1-a2 7. xx--11 = 2  \n2 -x +1  \n8. x-1 - 3 + x = 2 9. x-1 - 3 + x = 2 x +1 x x +1 x-1  \nx-3 x-3  \n-  \n10. 3 = 1 11. 2 4 = -1  \n1 x 1 x  \nx + x   \nx +1 x-1  \n2 + 1 -  \nx-2 x +1  \nSoluciones.  \n1. x=2  \n6. x= 1/2  \n11. x=1  \nx=2  \n2. x=3  \n7. x=3  \n3. x=0  \n8. x=3  \nx=-1/2  \n4. x=0  \n9. x=-3  \nx=0  \n5. x=4  \n10. x= 1/2  \nx=3/2  \nI. E.S. Arroyo de la Miel Dpto de Matemáticas  \nECUACIONES IRRACIONALES  \n1.  \nx +  = 30 2.  \nx + 1 =  x + 9 3.  \n7-3x - x = 7  \n4.  \nx + 4 = 3 -  x-1 5.  \n5  + 3 = 2 x 6.  \n6x + 1 - 5 = 2 x  \n3  \n7.  \n4x + 5 -  3x + 1 = 1 8.  \n2x-1 +  x + 4 = 6 9.  \n1 +  x + 1 = x 3  \n10.  \nx3 - 2 x = x 11.  \nx-3 +  x + 4 =  \n4x + 1  \n12.  \n2  x + 4 =  5 x + 4 13.  \nx2 + 3x +7 = 5 14.  \n3 -  = x + 1  \n15.  \n2  2x-1 =  6x-5 +  2x-9 16.  \n2x + 5 + 6 = 3x + 3  \n17.  \n3x + 10 = 1 +  3x + 3 18.  \n3x-2 - 4 = 0  \n19.  \n2x + 1 = x - 1  \n20.  \n2x-1 +  2x + 1 = 1 21.  \n  2x-1  \n6x + 1 = 2  \n3x  \n21  \n6x + 1  \n-  \n22.  \n3  \nx  \n=  \n6  \n 3x + 4  \n23.  \n3  \n2   \nx  \n=  \n2x  \n2 +  \n24.  \nSoluciones:  \n1. x=25, x=36; 2. x=16; 3. x=-3, x=-14; 4. x=13/9; 5. x=9, x=1/4; 6. x=8, x=1/2; 7. x=5, x=1; 8. x=5, x=221; 9. x=15, x=0; 10. x=0, x3; 11. x=12; 12. x=12; 13. x=3, x=-6; 14. x=1, x=4; 15. x=5; 16. x=2/9, x=2; 17. x=2; 18. x=6; 19. x=4, x=0; 20. x=5/8;  \n21. x=4/3; 22. x=4; 23. x=4, x=1; 24. x=-2, x=3/7; 25. x=-1  \nx + 6 +  x + 11 =  5-10 x 25.  \nI. E.S. Arroyo de la Miel Dpto de Matemáticas  \nECUACIONES BICUADRADASY BICÚBICAS  \n1. x4-5x2+4=0 2. x4+2x2-3=0 3. x6-9x3+8=0  \n4. x6-26x3-27=0 5. 6x4+2x2-8=0 6. x4-4x2=0  \n7. 4x4-17x2+4=0 8. 9x4-3x2+4=0 9. x4-6x2-27=0  \n10. x6+7x3-8=0 11. x4-2x2-8=0 12. x6+28x3+27=0  \nSoluciones:  \n1. x1, x2; 2. x1; 3. x=2, x=1; 4. x=-1, x=3; 5. x1; 6. x=0, x2; 7. x2, x1/2 8. x1/3, x2  \n9. x3 10. x=1, x=-2 11. x2 12. x=-1, x=-3","cbCaiebEb8ZnCLvJ","https://ap.wps.com/l/cbCaiebEb8ZnCLvJ","pdf",329184,5,1,3,"Spanish","es",110,"# Ecuaciones racionales\n## Soluciones\n# Ecuaciones irracionales\n## Soluciones\n# Ecuaciones bicuadradas y bícubicas","[{\"question\":\"¿Qué temas de ecuaciones cubre el documento?\",\"answer\":\"Cubre ecuaciones racionales, ecuaciones irracionales y ecuaciones bicuadradas y bícubicas, cada una con ejercicios numerados.\"},{\"question\":\"¿Incluye el documento respuestas finales?\",\"answer\":\"Sí. Para cada sección aparece un bloque de “Soluciones” con los valores de x correspondientes a los ejercicios listados.\"},{\"question\":\"¿Cómo están organizados los ejercicios y las soluciones?\",\"answer\":\"Primero se listan las ecuaciones en orden (numeradas) y luego se proporcionan las soluciones, indicando los valores de x que satisfacen cada ecuación.\"}]","Ecuaciones Racionales Irracionales y Bicuadradas y Bícubicas | PDF",1784012773,{"code":4,"msg":31,"data":32},"ok",{"site_id":25,"language":24,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":29},"rational-irrational-biquadratic-and-bicubic-equations","",{"@graph":36,"@context":85},[37,53,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,50],{"item":41,"name":42,"@type":43,"position":21},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":47},"https://docshare.wps.com/es/document/","Document",2,{"item":49,"name":12,"@type":43,"position":22},"https://docshare.wps.com/es/document/examen/",{"item":51,"name":13,"@type":43,"position":52},"https://docshare.wps.com/es/document/rational-irrational-biquadratic-and-bicubic-equations/69232/",4,{"url":51,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":24,"description":14,"dateModified":61,"datePublished":62,"encodingFormat":60,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":41,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-07-30","2026-07-14",true,{"@type":65,"interactionType":66,"userInteractionCount":20},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"¿Qué temas de ecuaciones cubre el documento?","Question",{"text":75,"@type":76},"Cubre ecuaciones racionales, ecuaciones irracionales y ecuaciones bicuadradas y bícubicas, cada una con ejercicios numerados.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"¿Incluye el documento respuestas finales?",{"text":80,"@type":76},"Sí. Para cada sección aparece un bloque de “Soluciones” con los valores de x correspondientes a los ejercicios listados.",{"name":82,"@type":73,"acceptedAnswer":83},"¿Cómo están organizados los ejercicios y las soluciones?",{"text":84,"@type":76},"Primero se listan las ecuaciones en orden (numeradas) y luego se proporcionan las soluciones, indicando los valores de x que satisfacen cada ecuación.","https://schema.org",{"og:url":51,"og:type":87,"og:title":13,"og:site_name":58,"og:description":14},"article",{"robots":89,"canonical":51},"index,follow",{"doc_id":7,"site_id":25},{"code":4,"msg":5,"data":92},[93,98,102,104,108,112,116,120,124,128],{"id":94,"doc_module":4,"doc_module_name":46,"category_name":95,"show_sort_weight":96,"slug":97},39,"Cómic",60,"comic",{"id":99,"doc_module":4,"doc_module_name":46,"category_name":100,"show_sort_weight":96,"slug":101},43,"Estilo de Vida","lifestyle",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":96,"slug":103},"exam",{"id":105,"doc_module":4,"doc_module_name":46,"category_name":106,"show_sort_weight":96,"slug":107},44,"General","general",{"id":109,"doc_module":4,"doc_module_name":46,"category_name":110,"show_sort_weight":96,"slug":111},41,"Investigación e Informes","research-report",{"id":113,"doc_module":4,"doc_module_name":46,"category_name":114,"show_sort_weight":96,"slug":115},37,"Literatura","literature",{"id":117,"doc_module":4,"doc_module_name":46,"category_name":118,"show_sort_weight":96,"slug":119},22,"Relatos y Novelas","story-novel",{"id":121,"doc_module":4,"doc_module_name":46,"category_name":122,"show_sort_weight":96,"slug":123},42,"Religión y Espiritualidad","religion-spirituality",{"id":125,"doc_module":4,"doc_module_name":46,"category_name":126,"show_sort_weight":96,"slug":127},40,"Salud y Atención Médica","healthcare",{"id":129,"doc_module":4,"doc_module_name":46,"category_name":130,"show_sort_weight":96,"slug":131},24,"Tecnología","technology"]