{"ok":true,"question":{"id":21220,"question_uuid":"6dbb1526-b9c8-438b-b6b1-50ac08e6c98a","job_id":4,"source_file":"A中考/2026江苏中考期末数学试卷+答案85.pdf","source_page_start":3,"source_page_end":3,"source_bbox":"[43.25, 141.89, 277.2, 175.13]","subject_code":"math","grade_level":"JUNIOR","tree_code":"KT_JUNIOR_MATH_STANDARD","question_type":"subjective","canonical_json":"{\"year\": null, \"blocks\": [{\"type\": \"math_inline\", \"latex\": \"x^{2}\"}, {\"text\": \" 4x  4 1 先化简,再求值:  (1), x \", \"type\": \"text\"}, {\"type\": \"math_inline\", \"latex\": \"\\\\sqrt{3}\"}, {\"text\": \".\", \"type\": \"text\"}, {\"type\": \"math_inline\", \"latex\": \"x^{2}\"}, {\"text\": \" x x 1\", \"type\": \"text\"}, {\"type\": \"solution\", \"blocks\": [{\"type\": \"math_inline\", \"latex\": \"x^{2}\"}, {\"text\": \" 4x  4 1  (1)\", \"type\": \"text\"}, {\"type\": \"math_inline\", \"latex\": \"\\\\frac{x^{2}}{x} \\\\frac{x}{2}\"}, {\"text\": \" x \", \"type\": \"text\"}, {\"type\": \"math_inline\", \"latex\": \"1 \\\\frac{1)^{2}}{1)^{2}}\"}, {\"text\": \" \", \"type\": \"text\"}, {\"type\": \"math_inline\", \"latex\": \"\\\\frac{11}{1}\"}, {\"text\": \"（） x  x(x  x  \", \"type\": \"text\"}, {\"type\": \"math_inline\", \"latex\": \"\\\\frac{x}{xx}\"}, {\"text\": \"\", \"type\": \"text\"}, {\"type\": \"math_inline\", \"latex\": \"\\\\frac{x}{x} \\\\frac{1}{2}\"}, {\"text\": \"（ 2）  (  x  2 , \", \"type\": \"text\"}, {\"type\": \"math_inline\", \"latex\": \"x \\\\sqrt{3}\"}, {\"text\": \" 2 3 \", \"type\": \"text\"}, {\"type\": \"math_inline\", \"latex\": \"2 \\\\sqrt{3}\"}, {\"text\": \"当x \", \"type\": \"text\"}, {\"type\": \"math_inline\", \"latex\": \"\\\\sqrt{3}\"}, {\"text\": \"时原式,  .\", \"type\": \"text\"}, {\"type\": \"math_inline\", \"latex\": \"\\\\sqrt{3} 3\"}]}], \"source\": {\"bbox\": [43.25, 141.89, 277.2, 175.13], \"file\": \"A中考/2026江苏中考期末数学试卷+答案85.pdf\", \"regions\": [{\"bbox\": [43.25, 141.89, 277.2, 175.13], \"page\": 3}], \"section\": \"example\", \"page_end\": 3, \"page_start\": 3, \"section_label\": \"跟我学 关键母题，中考常考题型各个击破！\", \"answer_regions\": [{\"bbox\": [30.874000549316406, 254.85260009765625, 210.2400054931641, 428.7696228027344], \"page\": 3}], \"answer_original\": \"\", \"solution_original\": \"x^{2}  4x  4 1  (1) \\\\frac{x^{2}}{x} \\\\frac{x}{2}  x 1 \\\\frac{1)^{2}}{1)^{2}}   \\\\frac{11}{1} （） x  x(x  x   \\\\frac{x}{xx}  \\\\frac{x}{x} \\\\frac{1}{2} （ 2）  (  x  2 ,  x \\\\sqrt{3}  2 3  2 \\\\sqrt{3} 当x  \\\\sqrt{3}时原式,  . \\\\sqrt{3} 3\"}, \"version\": 1, \"grade_level\": \"JUNIOR\", \"number_label\": \"1\", \"subject_code\": \"math\", \"question_type\": \"subjective\", \"content_sha256\": \"263c79b0295c9ac8159d60f0ee16962e83f65d40dfefcd55bdf8f10a4635a540\"}","body_html":"<div>\\(x^{2}\\) 4x  4 1 先化简,再求值:  (1), x \\(\\sqrt{3}\\).\\(x^{2}\\) x x 1</div>","answer_html":"","ways_html":"\\(x^{2}\\) 4x  4 1  (1)\\(\\frac{x^{2}}{x} \\frac{x}{2}\\) x <span class=\"formula-fallback\">1 frac1)^21)^2</span> \\(\\frac{11}{1}\\)（） x  x(x  x  \\(\\frac{x}{xx}\\)\\(\\frac{x}{x} \\frac{1}{2}\\)（ 2）  (  x  2 , \\(x \\sqrt{3}\\) 2 3 \\(2 \\sqrt{3}\\)当x \\(\\sqrt{3}\\)时原式,  .\\(\\sqrt{3} 3\\)","explain_html":null,"difficulty":2,"score":null,"year":null,"parse_status":"PARSED","qa_status":"QUARANTINED","retry_count":0,"final_score":0.925,"error_message":"QA failed: FORMULA,COHERENCE,ANSWER","published_question_id":null,"content_sha256":"263c79b0295c9ac8159d60f0ee16962e83f65d40dfefcd55bdf8f10a4635a540","created_at":"2026-09-24T23:22:50","updated_at":"2026-09-24T23:59:29","answer_missing":true,"formula_fallback":true,"_number":"1","_section":"example","_section_label":"跟我学 关键母题，中考常考题型各个击破！"},"assets":[],"knowledge":[],"audits":[{"id":418658,"import_question_id":21220,"audit_type":"STRUCTURE","auditor_name":"structure-auditor","status":"PASS","score":0.9,"input_snapshot":"x^{2}  4x  4 1 先化简,再求值:  (1), x  \\sqrt{3} . x^{2}  x x 1","result_json":"{\"ok\": true, \"issues\": [], \"confidence\": 0.9}","created_at":"2026-09-24T23:56:48"},{"id":418659,"import_question_id":21220,"audit_type":"FORMULA","auditor_name":"formula-auditor","status":"FAIL","score":1.0,"input_snapshot":"x^{2}; \\sqrt{3}; x^{2}; x^{2}; \\frac{x^{2}}{x} \\frac{x}{2}","result_json":"{\"risky\": 13, \"issues\": [\"非法 LaTeX #6: unbalanced delimiters\"], \"checked\": 13, \"invalid\": 1, \"visual_check\": \"delegated_to_question_vision\", \"invalid_details\": [{\"index\": 5, \"latex\": \"1 \\\\frac{1)^{2}}{1)^{2}}\", \"issues\": [\"unbalanced delimiters\"]}], \"visually_verified\": 0}","created_at":"2026-09-24T23:56:48"},{"id":418660,"import_question_id":21220,"audit_type":"KNOWLEDGE","auditor_name":"knowledge-auditor","status":"WARN","score":0.0,"input_snapshot":"x^{2}  4x  4 1 先化简,再求值:  (1), x  \\sqrt{3} . x^{2}  x x 1","result_json":"{\"picks\": [], \"tree_code\": \"KT_JUNIOR_MATH_STANDARD\", \"candidates\": 0, \"classifier_version\": null}","created_at":"2026-09-24T23:56:48"},{"id":418668,"import_question_id":21220,"audit_type":"VISION","auditor_name":"vision-auditor","status":"PASS","score":0.9,"input_snapshot":"题干：\n\\(x^{2}\\) 4x  4 1 先化简,再求值:  (1), x \\(\\sqrt{3}\\).\\(x^{2}\\) x x 1\n答案：\n\n解析：\n\\(x^{2}\\) 4x  4 1  (1)\\(\\frac{x^{2}}{x} \\frac{x}{2}\\) x  1 frac1)^21)^2  \\(\\frac{11}{1}\\)（） x  x(x  x  \\(\\frac{x}{xx}\\)\\(\\frac{x}{x} \\frac{1}{2}\\)（ 2）  (  x  2 , \\(x \\sqrt{3}\\) 2 3 \\(2 \\sqrt{3}\\)当x \\(\\sqrt{3}\\)时原式,  .\\(\\sqrt{3} 3\\)","result_json":"{\"ok\": true, \"hard\": false, \"issues\": [], \"confidence\": 0.9, \"suggestions\": [\"解析部分的排版较为混乱，建议优化公式布局以提升可读性\"]}","created_at":"2026-09-24T23:57:39"},{"id":418684,"import_question_id":21220,"audit_type":"SOLVER","auditor_name":"blind-solver","status":"PASS","score":1.0,"input_snapshot":"x^{2}  4x  4 1 先化简,再求值:  (1), x  \\sqrt{3} . x^{2}  x x 1","result_json":"{\"basis\": \"原式 = \\\\frac{(x-2)^2}{x(x-1)} \\\\div \\\\frac{x-2}{x-1} = \\\\frac{(x-2)^2}{x(x-1)} \\\\cdot \\\\frac{x-1}{x-2} = \\\\frac{x-2}{x}。当 x = \\\\sqrt{3} 时，代入得 \\\\frac{\\\\sqrt{3}-2}{\\\\sqrt{3}}。\", \"answer\": \"化简结果：\\\\frac{x-2}{x}；求值结果：\\\\frac{\\\\sqrt{3}-2}{\\\\sqrt{3}}\", \"confidence\": 1.0, \"handout_chars\": 0}","created_at":"2026-09-24T23:58:28"},{"id":418685,"import_question_id":21220,"audit_type":"CRITIC","auditor_name":"critic","status":"PASS","score":1.0,"input_snapshot":"来源答案: || 盲解:化简结果：\\frac{x-2}{x}；求值结果：\\frac{\\sqrt{3}-2}{\\sqrt{3}}","result_json":"{\"ok\": true, \"issues\": [], \"merged\": true, \"confidence\": 1.0}","created_at":"2026-09-24T23:58:28"},{"id":418686,"import_question_id":21220,"audit_type":"SYMBOLIC","auditor_name":"symbolic-auditor","status":"WARN","score":0.5,"input_snapshot":"答案: || 盲解:化简结果：\\frac{x-2}{x}；求值结果：\\frac{\\sqrt{3}-2}{\\sqrt{3}}","result_json":"{\"checks\": [], \"detail\": {\"reason\": \"未提取到来源答案\"}, \"status\": \"WARN\", \"applicable\": true}","created_at":"2026-09-24T23:58:28"},{"id":418719,"import_question_id":21220,"audit_type":"COHERENCE","auditor_name":"coherence-auditor","status":"FAIL","score":0.9,"input_snapshot":"答案: || 解析:\\(x^{2}\\) 4x  4 1  (1)\\(\\frac{x^{2}}{x} \\frac{x}{2}\\) x  1 frac1)^21)^2  \\(\\frac{11}{1}\\)（） x  x(x  x  \\(\\frac{x}{xx}\\)\\(\\frac{x}{x} \\frac{1}{2}\\)（ 2）  (  x  2 , \\(x \\sqrt{3}\\) 2","result_json":"{\"ok\": false, \"which\": [\"solution\"], \"issues\": [\"解析步骤混乱，未正确展示化简和求值过程，最终结果错误。\", \"原式 = \\\\frac{(x-2)^2}{x^2-x} \\\\div \\\\frac{x-2}{x}: 解析中未正确写出化简步骤，直接跳到了错误的中间结果 \\\\frac{x}{x} \\\\cdot \\\\frac{1}{2}（-2），逻辑混乱。\", \"\\\\frac{(x-2)^2}{x(x-1)} \\\\div \\\\frac{x-2}{x} = \\\\frac{x-2}{x-1}: 解析中未正确展示约分过程，导致后续计算错误。\", \"当 x = \\\\sqrt{3} 时，原式 = \\\\frac{\\\\sqrt{3}-2}{\\\\sqrt{3}}: 解析中最终结果为 \\\\sqrt{3} 3，与正确答案 \\\\frac{\\\\sqrt{3}-2}{\\\\sqrt{3}} 不符。\"], \"confidence\": 0.9, \"equation_checks\": [{\"valid\": false, \"reason\": \"解析中未正确写出化简步骤，直接跳到了错误的中间结果 \\\\frac{x}{x} \\\\cdot \\\\frac{1}{2}（-2），逻辑混乱。\", \"equation\": \"原式 = \\\\frac{(x-2)^2}{x^2-x} \\\\div \\\\frac{x-2}{x}\"}, {\"valid\": false, \"reason\": \"解析中未正确展示约分过程，导致后续计算错误。\", \"equation\": \"\\\\frac{(x-2)^2}{x(x-1)} \\\\div \\\\frac{x-2}{x} = \\\\frac{x-2}{x-1}\"}, {\"valid\": false, \"reason\": \"解析中最终结果为 \\\\sqrt{3} 3，与正确答案 \\\\frac{\\\\sqrt{3}-2}{\\\\sqrt{3}} 不符。\", \"equation\": \"当 x = \\\\sqrt{3} 时，原式 = \\\\frac{\\\\sqrt{3}-2}{\\\\sqrt{3}}\"}]}","created_at":"2026-09-24T23:59:29"},{"id":418720,"import_question_id":21220,"audit_type":"QUALITY_GATE","auditor_name":"quality-gate","status":"FAIL","score":0.925,"input_snapshot":"","result_json":"{\"warnings\": [], \"graded_gate\": true, \"hard_failed\": [\"FORMULA\", \"COHERENCE\", \"ANSWER\"]}","created_at":"2026-09-24T23:59:29"}]}