题目

A student was one day taking a walk with a professor. The professor was very popular with students for his ways of   11  . As they were walking, they saw lying in the path a pair of old shoes, which they   12   belonged to a poor man who was working in a field close by. The student turned to the professor, saying, “Let’s play a   13   on him: we’ll hide his shoes, and hide ourselves behind those bushes, and wait to see his   14   when he cannot find them.” The professor said, “We should   15   amuse ourselves at the expense of the poor. You are   16  , 方程loga（x+1）+x2=2（0＜a＜1）的解的个数________．