题目 #21544

UUID: d253da3f-0b56-41f0-aef0-418d75223d71
来源: 人教版/七下/2026江苏七年级期末数学试卷+答案440.pdf 第 3 页，bbox [30.0, 119.79, 277.37, 133.24]
题型 / 学科: fill_blank / math / JUNIOR
知识树: KT_JUNIOR_MATH_STANDARD
难度: 难度 2 / 5 简单 · 单一知识点
QA 状态: PUBLISHED 重试 0 次，得分 0.925
最终题 ID: 10065

最终题干渲染（f_body 预览）

已知\(|2x - \sqrt{3}| = \sqrt{2}\)，则实数\(x\)的值为____

答案 / 解析

答案（f_answer）

x =\(\frac{\sqrt{3} + \sqrt{2}}{2}\)或 x =\(\frac{\sqrt{3} - \sqrt{2}}{2}\)

解析（f_ways）

由 |2x -\(\sqrt{3}| = \sqrt{2}\)得 2x -\(\sqrt{3} = \sqrt{2}\)或 2x -\(\sqrt{3} = -\sqrt{2}\)。情形一：2x -\(\sqrt{3} = \sqrt{2} \Rightarrow 2x = \sqrt{3} + \sqrt{2} \Rightarrow\)x =\(\frac{\sqrt{3} + \sqrt{2}}{2}\)。情形二：2x -\(\sqrt{3} = -\sqrt{2} \Rightarrow 2x = \sqrt{3} - \sqrt{2} \Rightarrow\)x =\(\frac{\sqrt{3} - \sqrt{2}}{2}\)。经检验，两解均满足原方程。故实数 x 的值为\(\frac{\sqrt{3} + \sqrt{2}}{2}\)或\(\frac{\sqrt{3} - \sqrt{2}}{2}\)。

原图与资产（0）

该题没有裁出图片资产

审计记录

阶段	审计器	结果	得分
STRUCTURE	structure-rule	PASS	0.900
FORMULA	formula-auditor	PASS	1.000
KNOWLEDGE	knowledge-auditor	WARN	-
VISION	vision-auditor	PASS	0.900
SOLVER	blind-solver	PASS	1.000
CRITIC	critic	PASS	1.000
SYMBOLIC	symbolic-auditor	WARN	0.500
COHERENCE	coherence-auditor	FAIL	0.900
QUALITY_GATE	quality-gate	FAIL	0.925
SOLVER	blind-solver	PASS	1.000
CRITIC	critic	PASS	1.000
COHERENCE	coherence-auditor	PASS	1.000
SYMBOLIC	symbolic-auditor	WARN	0.550
AUTO_REPAIR_ATTEMPT	answer-repair	PASS	1.000
AUTO_REPAIR	answer-repair	PASS	1.000
VISION	vision-auditor	PASS	1.000

知识点（0）

无

正式题库记录（t_question.f_id=10065）

f_qkey: 3c014ee681b648daff33802769856102
f_style / 难度: 3 / 2
入库题干: 已知\(|2x - \sqrt{3}| = \sqrt{2}\)，则实数\(x\)的值为____
入库答案: x =\(\frac{\sqrt{3} + \sqrt{2}}{2}\)或 x =\(\frac{\sqrt{3} - \sqrt{2}}{2}\)
入库解析: 由 |2x -\(\sqrt{3}| = \sqrt{2}\)得 2x -\(\sqrt{3} = \sqrt{2}\)或 2x -\(\sqrt{3} = -\sqrt{2}\)。情形一：2x -\(\sqrt{3} = \sqrt{2} \Rightarrow 2x = \sqrt{3} + \sqrt{2} \Rightarrow\)x =\(\frac{\sqrt{3} + \sqrt{2}}{2}\)。情形二：2x -\(\sqrt{3} = -\sqrt{2} \Rightarrow 2x = \sqrt{3} - \sqrt{2} \Rightarrow\)x =\(\frac{\sqrt{3} - \sqrt{2}}{2}\)。经检验，两解均满足原方程。故实数 x 的值为\(\frac{\sqrt{3} + \sqrt{2}}{2}\)或\(\frac{\sqrt{3} - \sqrt{2}}{2}\)。

事件

时间	阶段	级别	消息
2026-09-25 02:01:16	PUBLISH	INFO	已发布 t_question.f_id=10065 qkey=3c014ee681b648daff33802769856102
2026-09-25 02:01:16	QA	INFO	QA: PASS (score=0.925)