diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json
index 061f69fb..481b5ee4 100644
--- a/题库0.3/Problems.json
+++ b/题库0.3/Problems.json
@@ -518625,6 +518625,31 @@
         "space": "",
         "unrelated": []
     },
+    "019897": {
+        "id": "019897",
+        "content": "已知函数$y=\\log_4(4^x+1)-\\dfrac{1}{2} x$, 当$x$取何值时函数值最小? 并求出该函数的最小值.",
+        "objs": [],
+        "tags": [
+            "第二单元"
+        ],
+        "genre": "4em",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高一校本作业必修第四章-20231023修改",
+        "edit": [
+            "20221230\t王伟叶",
+            "20231023\t王伟叶"
+        ],
+        "same": [],
+        "related": [
+            "020481"
+        ],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
     "020001": {
         "id": "020001",
         "content": "判断下列各组对象能否组成集合, 若能组成集合, 指出是有限集还是无限集.\\\\\n(1) 上海市控江中学$2022$年入学的全体高一年级新生;\\\\\n(2) 中国现有各省的名称;\\\\\n(3) 太阳、$2$、上海市;\\\\\n(4) 大于$10$且小于$15$的有理数;\\\\\n(5) 末位是$3$的自然数;\\\\\n(6) 影响力比较大的中国数学家;\\\\\n(7) 方程$x^2+x-3=0$的所有实数解;\\\\ \n(8) 函数$y=\\dfrac 1x$图像上所有的点;\\\\ \n(9) 在平面直角坐标系中, 到定点$(0, 0)$的距离等于$1$的所有点;\\\\\n(10) 不等式$3x-10<0$的所有正整数解;\\\\\n(11) 所有的平面四边形.",
@@ -532427,7 +532452,9 @@
             "20221230\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "019897"
+        ],
         "remark": "",
         "space": "4em",
         "unrelated": []