第一部分：数学
一、选择题
题目：若(a > 0, b > 0)，则下列不等式中正确的是：
- A. (a^2 + b^2 > 2ab)
- B. (a^2 + b^2 \leq 2ab)
- C. (a^2 + b^2 = 2ab)
- D. (a^2 + b^2 < 2ab)
答案解析：由均值不等式知，(a^2 + b^2 \geq 2ab)，当且仅当(a = b)时取等号。因此，正确答案是A。
题目：已知函数(f(x) = x^3 - 3x)，则(f’(x))的零点为：
- A. (x = -1)
- B. (x = 0)
- C. (x = 1)
- D. (x = 3)
答案解析：求导得(f’(x) = 3x^2 - 3)，令(f’(x) = 0)，解得(x = -1)或(x = 1)。因此，正确答案是A和C。
二、填空题
- 题目：已知(a, b)是方程(x^2 - 4x + 3 = 0)的两根，则(a^2 + b^2 = _____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________