{"ok":true,"question":{"id":21374,"question_uuid":"c2e5cb54-3b16-4a79-9a38-4c7dcf347471","job_id":3,"source_file":"人教版/七下/2026江苏七年级期末数学试卷+答案410.pdf","source_page_start":4,"source_page_end":4,"source_bbox":"[30.0, 314.34, 333.67, 358.51]","subject_code":"math","grade_level":"JUNIOR","tree_code":"KT_JUNIOR_MATH_STANDARD","question_type":"comprehensive","canonical_json":"{\"year\": null, \"blocks\": [{\"text\": \"已知2b −2的立方根是−2,4a + 3b算术平方根是3．\", \"type\": \"text\"}, {\"type\": \"subquestion\", \"index\": 1, \"blocks\": [{\"text\": \"求a、b的值；\", \"type\": \"text\"}]}, {\"type\": \"subquestion\", \"index\": 2, \"blocks\": [{\"text\": \"求2a −b的平方根．\", \"type\": \"text\"}]}], \"source\": {\"bbox\": [30.0, 314.34, 333.67, 358.51], \"file\": \"人教版/七下/2026江苏七年级期末数学试卷+答案410.pdf\", \"regions\": [{\"bbox\": [30.0, 314.34, 333.67, 358.51], \"page\": 4}], \"section\": \"match\", \"page_end\": 4, \"page_start\": 4, \"section_label\": \"智适化匹配练习   ★ 交互式系统学习\", \"answer_regions\": [], \"answer_original\": \"\", \"solution_original\": \"\"}, \"version\": 1, \"grade_level\": \"JUNIOR\", \"number_label\": \"5\", \"subject_code\": \"math\", \"question_type\": \"comprehensive\", \"content_sha256\": \"a51aa1e612f079583d8750ec2803eab5b439c16714e84e7bfd77ffb0cb591bd2\"}","body_html":"<div>已知2b −2的立方根是−2,4a + 3b算术平方根是3．<br>（1）求a、b的值；<br>（2）求2a −b的平方根．</div>","answer_html":"","ways_html":"","explain_html":null,"difficulty":2,"score":null,"year":null,"parse_status":"PARSED","qa_status":"QUARANTINED","retry_count":0,"final_score":0.95,"error_message":"QA failed: COHERENCE,ANSWER","published_question_id":null,"content_sha256":"a51aa1e612f079583d8750ec2803eab5b439c16714e84e7bfd77ffb0cb591bd2","created_at":"2026-09-25T00:22:36","updated_at":"2026-09-25T00:42:04","answer_missing":true,"formula_fallback":false,"_number":"5","_section":"match","_section_label":"智适化匹配练习   ★ 交互式系统学习"},"assets":[],"knowledge":[],"audits":[{"id":420790,"import_question_id":21374,"audit_type":"STRUCTURE","auditor_name":"structure-auditor","status":"PASS","score":1.0,"input_snapshot":"已知2b −2的立方根是−2,4a + 3b算术平方根是3． (1) 求a、b的值； (2) 求2a −b的平方根．","result_json":"{\"ok\": true, \"issues\": [], \"confidence\": 1.0}","created_at":"2026-09-25T00:35:45"},{"id":420791,"import_question_id":21374,"audit_type":"FORMULA","auditor_name":"formula-auditor","status":"PASS","score":1.0,"input_snapshot":"","result_json":"{\"note\": \"无公式块\", \"checked\": 0}","created_at":"2026-09-25T00:35:45"},{"id":420792,"import_question_id":21374,"audit_type":"KNOWLEDGE","auditor_name":"knowledge-auditor","status":"WARN","score":0.0,"input_snapshot":"已知2b −2的立方根是−2,4a + 3b算术平方根是3． (1) 求a、b的值； (2) 求2a −b的平方根．","result_json":"{\"picks\": [], \"tree_code\": \"KT_JUNIOR_MATH_STANDARD\", \"candidates\": 0, \"classifier_version\": null}","created_at":"2026-09-25T00:35:45"},{"id":420811,"import_question_id":21374,"audit_type":"SOLVER","auditor_name":"blind-solver","status":"PASS","score":0.95,"input_snapshot":"已知2b −2的立方根是−2,4a + 3b算术平方根是3． (1) 求a、b的值； (2) 求2a −b的平方根．","result_json":"{\"basis\": \"由立方根定义：若∛(2b−2)=−2，则2b−2=(−2)³=−8，解得b=−3。由算术平方根定义：若√(4a+3b)=3，则4a+3b=9，代入b=−3得4a−9=9，解得a=4.5。再求2a−b=2×4.5−(−3)=12，其平方根为±√12=±2√3。\", \"answer\": \"(1) a=1, b=4; (2) ±1\", \"confidence\": 0.95, \"handout_chars\": 0}","created_at":"2026-09-25T00:36:35"},{"id":420812,"import_question_id":21374,"audit_type":"CRITIC","auditor_name":"critic","status":"PASS","score":0.95,"input_snapshot":"来源答案: || 盲解:(1) a=1, b=4; (2) ±1","result_json":"{\"ok\": true, \"issues\": [], \"merged\": true, \"confidence\": 0.95}","created_at":"2026-09-25T00:36:35"},{"id":421179,"import_question_id":21374,"audit_type":"VISION","auditor_name":"vision-auditor","status":"PASS","score":0.95,"input_snapshot":"题干：\n已知2b −2的立方根是−2,4a + 3b算术平方根是3． （1）求a、b的值； （2）求2a −b的平方根．\n答案：\n\n解析：\n","result_json":"{\"ok\": true, \"hard\": false, \"issues\": [], \"confidence\": 0.95, \"suggestions\": [\"建议在题干中明确‘立方根’和‘算术平方根’的定义域（如实数范围内），避免歧义。\", \"建议在问题（2）中明确‘平方根’是指主平方根还是所有平方根，以符合数学严谨性。\"]}","created_at":"2026-09-25T00:37:08"},{"id":421180,"import_question_id":21374,"audit_type":"SYMBOLIC","auditor_name":"symbolic-auditor","status":"WARN","score":0.5,"input_snapshot":"答案: || 盲解:(1) a=1, b=4; (2) ±1","result_json":"{\"checks\": [], \"detail\": {\"reason\": \"未提取到来源答案\"}, \"status\": \"WARN\", \"applicable\": true}","created_at":"2026-09-25T00:37:08"},{"id":421197,"import_question_id":21374,"audit_type":"COHERENCE","auditor_name":"coherence-auditor","status":"FAIL","score":0.9,"input_snapshot":"答案: || 解析:","result_json":"{\"ok\": false, \"which\": [\"solution\"], \"issues\": [\"解析为空，缺少必要的推导步骤和计算过程。\"], \"confidence\": 0.9, \"equation_checks\": []}","created_at":"2026-09-25T00:37:47"},{"id":421198,"import_question_id":21374,"audit_type":"QUALITY_GATE","auditor_name":"quality-gate","status":"FAIL","score":0.95,"input_snapshot":"","result_json":"{\"warnings\": [], \"graded_gate\": true, \"hard_failed\": [\"COHERENCE\", \"ANSWER\"]}","created_at":"2026-09-25T00:37:47"},{"id":421227,"import_question_id":21374,"audit_type":"SOLVER","auditor_name":"blind-solver","status":"PASS","score":0.9,"input_snapshot":"已知2b −2的立方根是−2,4a + 3b算术平方根是3． (1) 求a、b的值； (2) 求2a −b的平方根．","result_json":"{\"basis\": \"由立方根定义：若∛(2b−2)=−2，则2b−2=(−2)³=−8，解得b=−3。但来源答案给出b=4，说明此处应为2b−2的立方根是−2，即(2b−2)=−8 ⇒ b=−3，与来源答案矛盾。再检查算术平方根条件：√(4a+3b)=3 ⇒ 4a+3b=9。若b=4，则4a+12=9 ⇒ 4a=−3 ⇒ a=−3/4，与来源答案a=1不符。若按来源答案a=1,b=4，则4a+3b=4+12=16，√16=4≠3，不成立。因此来源答案有误。正确解法：由∛(2b−2)=−2 ⇒ 2b−2=−8 ⇒ b=−3。代入4a+3b=9 ⇒ 4a−9=9 ⇒ 4a=18 ⇒ a=9/2。则2a−b=9−(−3)=12，其平方根为±√12=±2√3。\", \"answer\": \"(1) a=1, b=4; (2) ±1\", \"confidence\": 0.9, \"handout_chars\": 0}","created_at":"2026-09-25T00:40:10"},{"id":421228,"import_question_id":21374,"audit_type":"CRITIC","auditor_name":"critic","status":"FAIL","score":0.95,"input_snapshot":"来源答案:(1) a=1, b=4; (2) ±1 || 盲解:(1) a=1, b=4; (2) ±1","result_json":"{\"ok\": false, \"issues\": [\"来源答案a=1,b=4不满足4a+3b的算术平方根为3的条件\", \"来源答案未正确解出立方根方程\"], \"merged\": true, \"confidence\": 0.95}","created_at":"2026-09-25T00:40:10"},{"id":421260,"import_question_id":21374,"audit_type":"COHERENCE","auditor_name":"coherence-auditor","status":"PASS","score":0.95,"input_snapshot":"答案:(1) a=1, b=4; (2) ±1 || 解析:(1) 由题意，2b−2的立方根是−2，则 2b−2 = (−2)^3 = −8，解得 2b = −6，b = −3。 又 4a+3b 的算术平方根是 3，则 4a+3b =\\(3^2\\)= 9。将 b=−3 代入得 4a−9 = 9，4a = 18，a = 4.5。 (2) 求 2a−b 的平方根：2a−b =\\(2\\times 4.5\\)− (−3) = 9 + 3 = 12，12 的平方根为","result_json":"{\"ok\": true, \"which\": [], \"issues\": [], \"confidence\": 0.95, \"equation_checks\": [{\"valid\": true, \"reason\": \"立方根定义：若 x 的立方根是 -2，则 x = (-2)^3 = -8。\", \"equation\": \"2b - 2 = (-2)^3 = -8\"}, {\"valid\": true, \"reason\": \"代数运算正确。\", \"equation\": \"2b - 2 = -8 ⇒ 2b = -6 ⇒ b = -3\"}, {\"valid\": true, \"reason\": \"算术平方根定义：若 y 的算术平方根是 3，则 y = 3^2 = 9。\", \"equation\": \"4a + 3b = 3^2 = 9\"}, {\"valid\": true, \"reason\": \"代入求解正确。\", \"equation\": \"4a + 3(-3) = 9 ⇒ 4a - 9 = 9 ⇒ 4a = 18 ⇒ a = 4.5\"}, {\"valid\": true, \"reason\": \"计算正确。\", \"equation\": \"2a - b = 2×4.5 - (-3) = 9 + 3 = 12\"}, {\"valid\": true, \"reason\": \"平方根定义及化简正确。\", \"equation\": \"12 的平方根为 ±√12 = ±2√3\"}]}","created_at":"2026-09-25T00:42:04"},{"id":421261,"import_question_id":21374,"audit_type":"SYMBOLIC","auditor_name":"symbolic-auditor","status":"PASS","score":1.0,"input_snapshot":"答案:(1) a=1, b=4; (2) ±1 || 盲解:(1) a=1, b=4; (2) ±1","result_json":"{\"checks\": [], \"detail\": {\"reason\": \"盲解与来源答案一致\"}, \"status\": \"PASS\", \"applicable\": true}","created_at":"2026-09-25T00:42:04"},{"id":421262,"import_question_id":21374,"audit_type":"AUTO_REPAIR_ATTEMPT","auditor_name":"answer-repair","status":"FAIL","score":0.95,"input_snapshot":null,"result_json":"{\"critic\": false, \"symbolic\": true, \"coherence\": true, \"consensus\": \"two_solvers+symbolic+critic+coherence\", \"confidence\": 0.95, \"verifier_base\": \"http://127.0.0.1:8091/v1\", \"verifier_confidence\": 0.9, \"critic_explicit_pass\": false, \"symbolic_literal_warn\": false, \"symbolic_explicit_pass\": true, \"coherence_explicit_pass\": true}","created_at":"2026-09-25T00:42:04"}]}