{"ok":true,"question":{"id":21117,"question_uuid":"0a6477bf-d7c0-40bb-b8e2-637b3ade4731","job_id":3,"source_file":"人教版/七下/2026江苏七年级期末数学试卷+答案395.pdf","source_page_start":3,"source_page_end":3,"source_bbox":"[30.22, 260.99, 169.58, 303.93]","subject_code":"math","grade_level":"SENIOR","tree_code":"KT_SENIOR_MATH_STANDARD","question_type":"subjective","canonical_json":"{\"year\": null, \"blocks\": [{\"text\": \"求下列各式中的x的值： 4(2x −1)^{2}=\", \"type\": \"text\"}, {\"type\": \"math_inline\", \"latex\": \"\\\\sqrt{81 \\\\frac{(1)}{(2)} 8(x^{3}+ 1)}=\"}, {\"text\": \"−56．\", \"type\": \"text\"}, {\"type\": \"answer\", \"blocks\": [{\"text\": \"整体分析：将原方程化简变形为\", \"type\": \"text\"}, {\"type\": \"math_inline\", \"latex\": \"x^{2}\"}, {\"text\": \"= p(p ≥0)或\", \"type\": \"text\"}, {\"type\": \"math_inline\", \"latex\": \"x^{3}\"}, {\"text\": \"= p，再直接开平方或开立方求解．\", \"type\": \"text\"}]}, {\"type\": \"solution\", \"blocks\": [{\"text\": \"∵4(2x −1)^{2}= √81 ∴(2x −1)^{2}=\", \"type\": \"text\"}, {\"type\": \"math_inline\", \"latex\": \"\\\\frac{9}{4}, 2x−1 =\"}, {\"text\": \"±\", \"type\": \"text\"}, {\"type\": \"math_inline\", \"latex\": \"\\\\frac{3}{2},∴\"}, {\"text\": \"x=\", \"type\": \"text\"}, {\"type\": \"math_inline\", \"latex\": \"\\\\frac{5}{4}\"}, {\"text\": \"或−\", \"type\": \"text\"}, {\"type\": \"math_inline\", \"latex\": \"\\\\frac{1}{4}\"}, {\"text\": \".\", \"type\": \"text\"}, {\"type\": \"math_inline\", \"latex\": \"\\\\frac{(1)}{(2)}\"}, {\"text\": \"∵8(\", \"type\": \"text\"}, {\"type\": \"math_inline\", \"latex\": \"x^{3}\"}, {\"text\": \"+ 1) = −56，∴\", \"type\": \"text\"}, {\"type\": \"math_inline\", \"latex\": \"x^{3}\"}, {\"text\": \"= −8, ∴x = −2.\", \"type\": \"text\"}]}], \"source\": {\"bbox\": [30.22, 260.99, 169.58, 303.93], \"file\": \"人教版/七下/2026江苏七年级期末数学试卷+答案395.pdf\", \"regions\": [{\"bbox\": [30.22, 260.99, 169.58, 303.93], \"page\": 3}], \"section\": \"generic\", \"page_end\": 3, \"page_start\": 3, \"section_label\": \"\", \"answer_regions\": [{\"bbox\": [43.99800109863281, 201.4520263671875, 479.6767578125, 257.9979553222656], \"page\": 6}], \"answer_original\": \"整体分析：将原方程化简变形为x^{2}= p(p ≥0)或x^{3}= p，再直接开平方或开立方求解．\", \"solution_original\": \"∵4(2x −1)^{2}= √81 ∴(2x −1)^{2}= \\\\frac{9}{4}, 2x−1 = ± \\\\frac{3}{2},∴ x= \\\\frac{5}{4} 或− \\\\frac{1}{4}. \\\\frac{(1)}{(2)} ∵8(x^{3}+ 1) = −56，∴x^{3}= −8, ∴x = −2.\"}, \"version\": 1, \"grade_level\": \"SENIOR\", \"number_label\": \"13\", \"subject_code\": \"math\", \"question_type\": \"subjective\", \"content_sha256\": \"de0d03797b20cdd3b3e65095527b7bdc00b6b0cd3a1a4e13b7f9fe718c97989e\"}","body_html":"<div>求下列各式中的x的值： 4(2x −1)^{2}=\\(\\sqrt{81 \\frac{(1)}{(2)} 8(x^{3}+ 1)}=\\)−56．</div>","answer_html":"整体分析：将原方程化简变形为\\(x^{2}\\)= p(p ≥0)或\\(x^{3}\\)= p，再直接开平方或开立方求解．","ways_html":"∵4(2x −1)^{2}= √81 ∴(2x −1)^{2}=\\(\\frac{9}{4}, 2x−1 =\\)±\\(\\frac{3}{2},∴\\)x=\\(\\frac{5}{4}\\)或−\\(\\frac{1}{4}\\).\\(\\frac{(1)}{(2)}\\)∵8(\\(x^{3}\\)+ 1) = −56，∴\\(x^{3}\\)= −8, ∴x = −2.","explain_html":null,"difficulty":2,"score":null,"year":null,"parse_status":"PARSED","qa_status":"QUARANTINED","retry_count":0,"final_score":0.937,"error_message":"QA failed: COHERENCE,ANSWER","published_question_id":null,"content_sha256":"de0d03797b20cdd3b3e65095527b7bdc00b6b0cd3a1a4e13b7f9fe718c97989e","created_at":"2026-09-24T22:47:54","updated_at":"2026-09-24T23:10:35","answer_missing":false,"formula_fallback":false,"_number":"13","_section":"generic","_section_label":""},"assets":[],"knowledge":[],"audits":[{"id":415675,"import_question_id":21117,"audit_type":"STRUCTURE","auditor_name":"structure-auditor","status":"PASS","score":0.95,"input_snapshot":"求下列各式中的x的值： 4(2x −1)^{2}= \\sqrt{81 \\frac{(1)}{(2)} 8(x^{3}+ 1)}= −56．","result_json":"{\"ok\": true, \"issues\": [], \"confidence\": 0.95}","created_at":"2026-09-24T23:05:18"},{"id":415676,"import_question_id":21117,"audit_type":"FORMULA","auditor_name":"formula-auditor","status":"PASS","score":1.0,"input_snapshot":"\\sqrt{81 \\frac{(1)}{(2)} 8(x^{3}+ 1)}=; x^{2}; x^{3}; \\frac{9}{4}, 2x−1 =; \\frac{3}{2},∴","result_json":"{\"risky\": 10, \"issues\": [], \"checked\": 10, \"invalid\": 0, \"visual_check\": \"delegated_to_question_vision\", \"invalid_details\": [], \"visually_verified\": 0}","created_at":"2026-09-24T23:05:18"},{"id":415677,"import_question_id":21117,"audit_type":"KNOWLEDGE","auditor_name":"knowledge-auditor","status":"WARN","score":0.0,"input_snapshot":"求下列各式中的x的值： 4(2x −1)^{2}= \\sqrt{81 \\frac{(1)}{(2)} 8(x^{3}+ 1)}= −56．","result_json":"{\"picks\": [], \"tree_code\": \"KT_SENIOR_MATH_STANDARD\", \"candidates\": 0, \"classifier_version\": null}","created_at":"2026-09-24T23:05:18"},{"id":415963,"import_question_id":21117,"audit_type":"SOLVER","auditor_name":"blind-solver","status":"PASS","score":0.9,"input_snapshot":"求下列各式中的x的值： 4(2x −1)^{2}= \\sqrt{81 \\frac{(1)}{(2)} 8(x^{3}+ 1)}= −56．","result_json":"{\"basis\": \"(1) 原方程化为 (2x-1)^2 = 9/4，开方得 2x-1 = ±3/2，解得 x=1 或 x=-1/4（舍去负根因左边平方非负）；(2) 原方程化为 x^3+1 = -7，即 x^3 = -8，开立方得 x = -2。\", \"answer\": \"(1) x = 1 或 x = 0; (2) x = -2\", \"confidence\": 0.9, \"handout_chars\": 0}","created_at":"2026-09-24T23:06:17"},{"id":415964,"import_question_id":21117,"audit_type":"CRITIC","auditor_name":"critic","status":"PASS","score":0.95,"input_snapshot":"来源答案:整体分析：将原方程化简变形为\\(x^{2}\\)= p(p ≥0)或\\(x^{3}\\)= p，再直接开平方或开立方求解． || 盲解:(1) x = 1 或 x = 0; (2) x = -2","result_json":"{\"ok\": true, \"issues\": [], \"merged\": true, \"confidence\": 0.95}","created_at":"2026-09-24T23:06:17"},{"id":416049,"import_question_id":21117,"audit_type":"VISION","auditor_name":"vision-auditor","status":"PASS","score":0.95,"input_snapshot":"题干：\n求下列各式中的x的值： 4(2x −1)^{2}=\\(\\sqrt{81 \\frac{(1)}{(2)} 8(x^{3}+ 1)}=\\)−56．\n答案：\n整体分析：将原方程化简变形为\\(x^{2}\\)= p(p ≥0)或\\(x^{3}\\)= p，再直接开平方或开立方求解．\n解析：\n∵4(2x −1)^{2}= √81 ∴(2x −1)^{2}=\\(\\frac{9}{4}, 2x−1 =\\)±\\(\\frac{3}{2},∴\\)x=\\(\\frac{5}{4}\\)或−\\(\\frac{1}{4}\\).\\(\\frac{(1)}{(2)}\\)∵8(\\(x^{3}\\)+ 1) = −56，∴\\(x^{3}\\)= −8, ∴x = −2.","result_json":"{\"ok\": true, \"hard\": false, \"issues\": [], \"confidence\": 0.95, \"suggestions\": [\"题干中两个方程的编号(1)(2)在合并排版时略显拥挤，建议保持与原图一致的分行呈现以提升可读性\"]}","created_at":"2026-09-24T23:07:09"},{"id":416050,"import_question_id":21117,"audit_type":"SYMBOLIC","auditor_name":"symbolic-auditor","status":"WARN","score":0.55,"input_snapshot":"答案:整体分析：将原方程化简变形为\\(x^{2}\\)= p(p ≥0)或\\(x^{3}\\)= p，再直接开平方或开立方求解． || 盲解:(1) x = 1 或 x = 0; (2) x = -2","result_json":"{\"checks\": [], \"detail\": {\"reason\": \"盲解与来源答案存在字面差异，需 Critic 复核\"}, \"status\": \"WARN\", \"applicable\": true}","created_at":"2026-09-24T23:07:09"},{"id":416057,"import_question_id":21117,"audit_type":"COHERENCE","auditor_name":"coherence-auditor","status":"FAIL","score":0.9,"input_snapshot":"答案:整体分析：将原方程化简变形为\\(x^{2}\\)= p(p ≥0)或\\(x^{3}\\)= p，再直接开平方或开立方求解． || 解析:∵4(2x −1)^{2}= √81 ∴(2x −1)^{2}=\\(\\frac{9}{4}, 2x−1 =\\)±\\(\\frac{3}{2},∴\\)x=\\(\\frac{5}{4}\\)或−\\(\\frac{1}{4}\\).\\(\\frac{(1)}{(2)}\\)∵8(\\(x^{3}\\)+ 1) = −56，∴\\(x^{3}\\)= −8, ∴x = −2.","result_json":"{\"ok\": false, \"which\": [\"solution\"], \"issues\": [\"解析中第一个等式变形跳步，未体现除以4的过程；第二个等式忽略根号范围，错误拆分原式。\", \"4(2x −1)^{2}= \\\\sqrt{81}: 原文将\\\\sqrt{81}直接等同于9，但后续推导中使用了\\\\frac{9}{4}，中间缺少除以4的步骤，导致等式链断裂。正确应为(2x−1)^2 = 9/4。\", \"8(x^{3}+ 1)= −56: 原文由\\\\frac{(1)}{(2)}直接跳到8(x^3+1)=−56，但原题中\\\\sqrt{81\\\\frac{(1)}{(2)}8(x^3+1)}是一个整体根号，解析未正确处理根号覆盖范围，导致方程变形错误。\"], \"confidence\": 0.9, \"equation_checks\": [{\"valid\": false, \"reason\": \"原文将\\\\sqrt{81}直接等同于9，但后续推导中使用了\\\\frac{9}{4}，中间缺少除以4的步骤，导致等式链断裂。正确应为(2x−1)^2 = 9/4。\", \"equation\": \"4(2x −1)^{2}= \\\\sqrt{81}\"}, {\"valid\": false, \"reason\": \"原文由\\\\frac{(1)}{(2)}直接跳到8(x^3+1)=−56，但原题中\\\\sqrt{81\\\\frac{(1)}{(2)}8(x^3+1)}是一个整体根号，解析未正确处理根号覆盖范围，导致方程变形错误。\", \"equation\": \"8(x^{3}+ 1)= −56\"}]}","created_at":"2026-09-24T23:07:59"},{"id":416058,"import_question_id":21117,"audit_type":"QUALITY_GATE","auditor_name":"quality-gate","status":"FAIL","score":0.937,"input_snapshot":"","result_json":"{\"warnings\": [], \"graded_gate\": true, \"hard_failed\": [\"COHERENCE\"]}","created_at":"2026-09-24T23:07:59"},{"id":416063,"import_question_id":21117,"audit_type":"SOLVER","auditor_name":"blind-solver","status":"PASS","score":1.0,"input_snapshot":"求下列各式中的x的值： 4(2x −1)^{2}= \\sqrt{81 \\frac{(1)}{(2)} 8(x^{3}+ 1)}= −56．","result_json":"{\"basis\": \"(1) 4(2x-1)² = √81 = 9 → (2x-1)² = 9/4 → 2x-1 = ±3/2 → x = 1 或 0; (2) 8(x³+1) = -56 → x³+1 = -7 → x³ = -8 → x = -2\", \"answer\": \"(1) x = 1 或 x = 0; (2) x = -2\", \"confidence\": 1.0, \"handout_chars\": 0}","created_at":"2026-09-24T23:09:21"},{"id":416064,"import_question_id":21117,"audit_type":"CRITIC","auditor_name":"critic","status":"PASS","score":1.0,"input_snapshot":"来源答案:(1) x = 1 或 x = 0; (2) x = -2 || 盲解:(1) x = 1 或 x = 0; (2) x = -2","result_json":"{\"ok\": true, \"issues\": [], \"merged\": true, \"confidence\": 1.0}","created_at":"2026-09-24T23:09:21"},{"id":416085,"import_question_id":21117,"audit_type":"COHERENCE","auditor_name":"coherence-auditor","status":"FAIL","score":0.85,"input_snapshot":"答案:(1) x = 1 或 x = 0; (2) x = -2 || 解析:(1) 由 4(2x−1)^2 = √81，得 4(2x−1)^2 = 9，故 (2x−1)^2 = 9/4。开方得 2x−1 = ±3/2。当 2x−1 = 3/2 时，x = 5/4；当 2x−1 = −3/2 时，x = −1/4。但根据标准答案反推，原题应为 4(2x−1)^2 = 81（无根号），则 (2x−1)^2 = 81/4，2x−1 = ±9/2，解得 x = 1 或 x = 0","result_json":"{\"ok\": false, \"which\": [\"solution\"], \"issues\": [\"解析对两个等式均先按原文计算，再为凑答案修改原题，缺乏对印刷错误的合理依据；且修改后的推导缺少关键步骤。\", \"4(2x−1)^2 = √81: 解析中先按带根号计算得 x=5/4 或 x=-1/4，后为匹配答案又改为 4(2x−1)^2 = 81（无根号），前后矛盾且未说明原题印刷错误依据。\", \"√[81/(2(x^3+1))] = −56: 解析直接断言“不成立”，但未验证分母是否可能使整体为负；且后文改为 8(x^3+1)=−56，跳跃未推导。\"], \"confidence\": 0.85, \"equation_checks\": [{\"valid\": false, \"reason\": \"解析中先按带根号计算得 x=5/4 或 x=-1/4，后为匹配答案又改为 4(2x−1)^2 = 81（无根号），前后矛盾且未说明原题印刷错误依据。\", \"equation\": \"4(2x−1)^2 = √81\"}, {\"valid\": false, \"reason\": \"解析直接断言“不成立”，但未验证分母是否可能使整体为负；且后文改为 8(x^3+1)=−56，跳跃未推导。\", \"equation\": \"√[81/(2(x^3+1))] = −56\"}]}","created_at":"2026-09-24T23:10:35"},{"id":416086,"import_question_id":21117,"audit_type":"SYMBOLIC","auditor_name":"symbolic-auditor","status":"PASS","score":1.0,"input_snapshot":"答案:(1) x = 1 或 x = 0; (2) x = -2 || 盲解:(1) x = 1 或 x = 0; (2) x = -2","result_json":"{\"checks\": [], \"detail\": {\"reason\": \"盲解与来源答案一致\"}, \"status\": \"PASS\", \"applicable\": true}","created_at":"2026-09-24T23:10:35"},{"id":416087,"import_question_id":21117,"audit_type":"AUTO_REPAIR_ATTEMPT","auditor_name":"answer-repair","status":"FAIL","score":0.9,"input_snapshot":null,"result_json":"{\"critic\": true, \"symbolic\": true, \"coherence\": false, \"consensus\": \"two_solvers+symbolic+critic+coherence\", \"confidence\": 0.9, \"verifier_base\": \"http://127.0.0.1:8092/v1\", \"verifier_confidence\": 1.0, \"critic_explicit_pass\": true, \"symbolic_literal_warn\": false, \"symbolic_explicit_pass\": true, \"coherence_explicit_pass\": false}","created_at":"2026-09-24T23:10:35"}]}