{"ok":true,"question":{"id":21390,"question_uuid":"93c6b474-bce3-4c3b-81a9-0aabed4a9fc9","job_id":3,"source_file":"人教版/七下/2026江苏七年级期末数学试卷+答案415.pdf","source_page_start":2,"source_page_end":2,"source_bbox":"[30.22, 738.19, 354.0, 778.58]","subject_code":"math","grade_level":"JUNIOR","tree_code":"KT_JUNIOR_MATH_STANDARD","question_type":"subjective","canonical_json":"{\"year\": null, \"blocks\": [{\"text\": \"已知\", \"type\": \"text\"}, {\"type\": \"math_inline\", \"latex\": \"2x+1\"}, {\"text\": \"是\", \"type\": \"text\"}, {\"type\": \"math_inline\", \"latex\": \"49\"}, {\"text\": \"的算术平方根，x+4y-10\", \"type\": \"text\"}, {\"text\": \"的立方根是\\\\)-3．\\n(1) 求$x,y$的值；\\n(2) 求\\\\(2x-y的立方根．\", \"type\": \"text\"}, {\"type\": \"answer\", \"blocks\": [{\"text\": \"(1)x = 3, y = −5; (2)^{3}√11\", \"type\": \"text\"}]}, {\"type\": \"solution\", \"blocks\": [{\"text\": \"(1)∵ 2x+ 1是49的算术平方根， ∴ 2x+ 1 = √49 = 7,∴ x= 3,因为 x + 4y −10的立方根是−3, ∴3 + 4y −10 = (−3)^{3}, ∴y = −5; (2)由（1）得x= 3,y= −5,∴ 2x− y=\", \"type\": \"text\"}, {\"type\": \"math_inline\", \"latex\": \"2 \\\\times 3\"}, {\"text\": \"−(−5) = 11,所以2x −y的立方根是^{3}√11.\", \"type\": \"text\"}]}], \"source\": {\"bbox\": [30.22, 738.19, 354.0, 778.58], \"file\": \"人教版/七下/2026江苏七年级期末数学试卷+答案415.pdf\", \"regions\": [{\"bbox\": [30.22, 738.19, 354.0, 778.58], \"page\": 2}], \"section\": \"generic\", \"page_end\": 2, \"page_start\": 2, \"section_label\": \"\", \"answer_regions\": [{\"bbox\": [43.99800109863281, 136.1236572265625, 480.2902221679687, 192.1593475341797], \"page\": 5}], \"answer_original\": \"(1)x = 3, y = −5; (2)^{3}√11\", \"solution_original\": \"(1)∵ 2x+ 1是49的算术平方根， ∴ 2x+ 1 = √49 = 7,∴ x= 3,因为 x + 4y −10的立方根是−3, ∴3 + 4y −10 = (−3)^{3}, ∴y = −5; (2)由（1）得x= 3,y= −5,∴ 2x− y= 2 × 3 −(−5) = 11,所以2x −y的立方根是^{3}√11.\"}, \"version\": 1, \"grade_level\": \"JUNIOR\", \"number_label\": \"15\", \"subject_code\": \"math\", \"question_type\": \"subjective\", \"content_sha256\": \"ad87becc3f96955c59acf7f23d2e8f9dd01b26342d9b73e4d0bb7feaf7bc18bc\"}","body_html":"<div>已知\\(2x+1\\)是\\(49\\)的算术平方根，x+4y-10的立方根是\\)-3．\n(1) 求$x,y$的值；\n(2) 求<span class=\"formula-fallback\">2x-y的立方根．</span></div>","answer_html":"(1)x = 3, y = −5; (2)^{3}√11","ways_html":"(1)∵ 2x+ 1是49的算术平方根， ∴ 2x+ 1 = √49 = 7,∴ x= 3,因为 x + 4y −10的立方根是−3, ∴3 + 4y −10 = (−3)^{3}, ∴y = −5; (2)由（1）得x= 3,y= −5,∴ 2x− y=\\(2 \\times 3\\)−(−5) = 11,所以2x −y的立方根是^{3}√11.","explain_html":null,"difficulty":2,"score":null,"year":null,"parse_status":"PARSED","qa_status":"QUARANTINED","retry_count":0,"final_score":0.8,"error_message":"QA failed: VISION","published_question_id":null,"content_sha256":"ad87becc3f96955c59acf7f23d2e8f9dd01b26342d9b73e4d0bb7feaf7bc18bc","created_at":"2026-09-25T00:43:18","updated_at":"2026-09-25T01:02:05","answer_missing":false,"formula_fallback":true,"_number":"15","_section":"generic","_section_label":""},"assets":[],"knowledge":[],"audits":[{"id":421875,"import_question_id":21390,"audit_type":"STRUCTURE","auditor_name":"structure-auditor","status":"PASS","score":1.0,"input_snapshot":"已知 2x+1 是 49 的算术平方根，x+4y-10的立方根是\\)-3． (1) 求$x,y$的值； (2) 求\\(2x-y的立方根．","result_json":"{\"ok\": true, \"issues\": [], \"confidence\": 1.0}","created_at":"2026-09-25T00:59:58"},{"id":421876,"import_question_id":21390,"audit_type":"FORMULA","auditor_name":"formula-auditor","status":"PASS","score":1.0,"input_snapshot":"2x+1; 49; 2 \\times 3","result_json":"{\"risky\": 1, \"issues\": [], \"checked\": 3, \"invalid\": 0, \"visual_check\": \"delegated_to_question_vision\", \"invalid_details\": [], \"visually_verified\": 0}","created_at":"2026-09-25T00:59:58"},{"id":421877,"import_question_id":21390,"audit_type":"KNOWLEDGE","auditor_name":"knowledge-auditor","status":"WARN","score":0.0,"input_snapshot":"已知 2x+1 是 49 的算术平方根，x+4y-10的立方根是\\)-3． (1) 求$x,y$的值； (2) 求\\(2x-y的立方根．","result_json":"{\"picks\": [], \"tree_code\": \"KT_JUNIOR_MATH_STANDARD\", \"candidates\": 0, \"classifier_version\": null}","created_at":"2026-09-25T00:59:58"},{"id":421878,"import_question_id":21390,"audit_type":"SOLVER","auditor_name":"blind-solver","status":"PASS","score":1.0,"input_snapshot":"已知 2x+1 是 49 的算术平方根，x+4y-10的立方根是\\)-3． (1) 求$x,y$的值； (2) 求\\(2x-y的立方根．","result_json":"{\"basis\": \"由题意，2x+1 是 49 的算术平方根，故 2x+1=7，解得 x=3。又 x+4y-10 的立方根是 -3，即 x+4y-10 = (-3)^3 = -27，代入 x=3 得 3+4y-10=-27，解得 y=-5。于是 2x-y = 2*3 - (-5) = 11，其立方根为 \\\\sqrt[3]{11}。\", \"answer\": \"x=3, y=-5; 立方根为 \\\\sqrt[3]{11}\", \"confidence\": 1.0, \"handout_chars\": 0}","created_at":"2026-09-25T01:00:22"},{"id":421879,"import_question_id":21390,"audit_type":"CRITIC","auditor_name":"critic","status":"PASS","score":1.0,"input_snapshot":"来源答案:(1)x = 3, y = −5; (2)^{3}√11 || 盲解:x=3, y=-5; 立方根为 \\sqrt[3]{11}","result_json":"{\"ok\": true, \"issues\": [], \"merged\": true, \"confidence\": 1.0}","created_at":"2026-09-25T01:00:22"},{"id":421880,"import_question_id":21390,"audit_type":"VISION","auditor_name":"vision-auditor","status":"WARN","score":0.2,"input_snapshot":"题干：\n已知\\(2x+1\\)是\\(49\\)的算术平方根，x+4y-10的立方根是\\)-3． (1) 求$x,y$的值； (2) 求\\(2x-y的立方根．\n答案：\n(1)x = 3, y = −5; (2)^{3}√11\n解析：\n(1)∵ 2x+ 1是49的算术平方根， ∴ 2x+ 1 = √49 = 7,∴ x= 3,因为 x + 4y −10的立方根是−3, ∴3 + 4y −10 = (−3)^{3}, ∴y = −5; (2)由（1）得x= 3,y= −5,∴ 2x− y=\\(2 \\times 3\\)−(−5) = 11,所以2x −y的立方根是^{3}√11.","result_json":"{\"note\": \"视觉比对不可用\", \"error\": \"invalid_json\", \"unavailable\": true}","created_at":"2026-09-25T01:00:24"},{"id":421881,"import_question_id":21390,"audit_type":"SYMBOLIC","auditor_name":"symbolic-auditor","status":"WARN","score":0.55,"input_snapshot":"答案:(1)x = 3, y = −5; (2)^{3}√11 || 盲解:x=3, y=-5; 立方根为 \\sqrt[3]{11}","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":"2026-09-25T01:00:24"},{"id":421909,"import_question_id":21390,"audit_type":"COHERENCE","auditor_name":"coherence-auditor","status":"PASS","score":1.0,"input_snapshot":"答案:(1)x = 3, y = −5; (2)^{3}√11 || 解析:(1)∵ 2x+ 1是49的算术平方根， ∴ 2x+ 1 = √49 = 7,∴ x= 3,因为 x + 4y −10的立方根是−3, ∴3 + 4y −10 = (−3)^{3}, ∴y = −5; (2)由（1）得x= 3,y= −5,∴ 2x− y=\\(2 \\times 3\\)−(−5) = 11,所以2x −y的立方根是^{3}√11.","result_json":"{\"ok\": true, \"which\": [], \"issues\": [], \"confidence\": 1.0, \"equation_checks\": [{\"valid\": true, \"reason\": \"√49 的算术平方根是 7，等式成立。\", \"equation\": \"2x+1 = √49 = 7\"}, {\"valid\": true, \"reason\": \"由 2x+1=7 解得 x=3，正确。\", \"equation\": \"x = 3\"}, {\"valid\": true, \"reason\": \"x+4y−10 的立方根是−3，则 x+4y−10 = (−3)^3 = −27，代入 x=3 得 3+4y−10=−27，等式成立。\", \"equation\": \"3 + 4y −10 = (−3)^{3}\"}, {\"valid\": true, \"reason\": \"由 3+4y−10=−27 解得 4y=−20，y=−5，正确。\", \"equation\": \"y = −5\"}, {\"valid\": true, \"reason\": \"x=3, y=−5，则 2x−y = 2×3−(−5) = 6+5 = 11，正确。\", \"equation\": \"2x−y = 11\"}, {\"valid\": true, \"reason\": \"11 的立方根记作 ∛11，正确。\", \"equation\": \"2x−y 的立方根是 ^{3}√11\"}]}","created_at":"2026-09-25T01:02:05"},{"id":421910,"import_question_id":21390,"audit_type":"QUALITY_GATE","auditor_name":"quality-gate","status":"FAIL","score":0.8,"input_snapshot":"","result_json":"{\"warnings\": [], \"graded_gate\": true, \"hard_failed\": [\"VISION\"]}","created_at":"2026-09-25T01:02:05"}]}