2012年北京大学保送生测试数学部分的第3题为:题目已知f(x)为一元二次函数,且a,f(a),f(f(a)),f(f(f(a)))为正项等比数列.求证:f(a)=a.这是一道构思精巧的试题,涉及到一元二次函数、等比数列甚至复合函数、不动点等概念,很耐人寻味.文[1]利用一元二次函数的性质,给出试题的一种证法.本文将试题推广为下面的定理,并给出一个简证. The third question of the mathematics part of Peking University in Peking University in 2012 is that the subject has known that f (x) is a quadratic function of quadratic function, and f (a), f (f Proof: f (a) = a. This is an ingenious examination of questions involving concepts such as a quadratic function, an equal ratio series or even a complex function, fixed point, etc. It is intriguing . [1] By using the property of a quadratic function, a proof of test is given. In this paper, we generalize the test question to the following theorem and give a brief proof.