已知n2+5n+13是完全平方数，则自然数n的值为______．
假设：n2+5n+13=（n+k）2，
∴（n+k）2=n2+2nk+k2，
∴2nk+k2=5n+13，
∴n=
，k2-13 5-2k
如果n是自然数，则应该不小于0 （从式子里看出不等于0），
∴①k2＞13并且5＞2k（不存在）；
②k2＜13并且5＜2k，只能k=3，
此时n=4．
故答案为：4．
| 完形填空。 | |||
| Last year my English class was 1 for me. First of all, it wasn’t easy for me to understand the teacher when she 2 to the class. To begin with, she spoke too quickly, and I couldn’t 3 every word. Late  r on, I realized itdoesn’t matter if you don’t understand every word, 4 I was afraid to speak in class because I thought my classmates might laugh 5 me. I couldn’t always make complete sentences, either. Then I started to 6 English-language TV.It helped a lot. I think that doing lots of listening practice is one of the secrets of 7 a good language learner. Another thing that I found very difficult was English 8 . So I decided to take lots of grammar notes in every class. | |||
| ( )1. A. lucky ( )2. A. talked ( )3. A. think ( )4. A. either ( )5. A. to ( )6. A. watched ( )7. A. making ( )8. A. grammar | B. happy B. talk B. believe B. neither B. with B. watch B. becoming B. words | C. difficult C. sing C. forget C. also C. at C. watches C. changing C. pronunciation | D. great. D. sang D. understand D. too D. in D. watching D. turning D. tests |