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三角函数与一元二次方程巧妙结合,构成了灵活多样的综合题,旨在考查同学们综合运用知识解题的能力。 例1 已知α是锐角,且tanα,cotα是关于x的一元二次方程x~2-kx+k~2-8=0的两个实数根。求k的值。(2002年浙江省绍兴市中考题)
The combination of trigonometric functions and quadratic equations constitutes a flexible and comprehensive problem, designed to examine the ability of students to use knowledge to solve problems. Example 1 It is known that α is an acute angle, and tanα and cotα are two real roots of a one-dimensional quadratic equation x~2-kx+k~2-8=0 regarding x. Find the value of k. (2002 Zhejiang Shaoxing City Examination Questions)