（1）观察下列各式：62-42=4×5，112-92=4×10，172-152=4×16…试用你发现的规律填空：512-492=4×______，662-642=4×______；
（2）请你用含一个字母的等式将上面各式呈现的规律表示出来，并用所学数学知识说明你所写式子的正确性．
（1）由62-42=4×5，5界于4和6之间的正整数；
112-92=4×10，10界于11和9之间的正整数；
172-152=4×16，16界于17和15之间的正整数；
所以试着推出：512-492=4×50，50界于49和51之间的正整数，且左边=右边成立；
662-642=4×65，65界于64和66之间的正整数，且左边=右边成立；
（2）可以得出规律：（n+2）2-n2=4（n+1）；
左边=（n+2）2-n2=（n+2+n）（n+2-n）=4（n+1）=右边．
| 完形填空。 | |||
| A group of graduates got together to visit their old university professor.They talked about the 1 topic-happiness.But soon their conversation turned into complaints about 2 in work and life. To offer his guests coffee, the professor went to the kitchen and 3 with a large pot of coffee and a variety of 4 -plastic,glass, metal, porcelain (陶瓷), som plain-looking some very 5 .The professor told his students to help themselves to hot coffee. When all the students had a cup of coffee in 6 . the professor said:"lf you have noticed, all the nice-looking 7 . cups were taken, leaving behind the plain and cheap ones.While it is 8 for you to want only the best for Yourbelves, that is the 9 of your problems and stress.The professor continued," Believe that the cup itself adds no 10 to the coffee.ln most cases it is just more expensive and in some cases it even 11 what we drink.What all of you 12 wanted was coffee, not the cup, but you consciously went 13 the best cups.Now 14 this: life is coffee, the jobs, money,and 15 in society are the cups9 which are just tools to hold and 16 life, and the different typesof cups we have don't decide, nor 17 the quality oflife.lf we concentrate only on the cups, we will 18 to enjoy the coffee in it.So don't let the cups 19 you...enjoy the coffee instead." At these words, the graduates looked at each other in 20 embarrassment. | |||
| ( )1. A. hot ( )2. A. pay ( )3. A. cooked ( )4. A. cups ( )5. A. common ( )6. A. order ( )7. A. pretty ( )8. A. necessary ( )9. A. situation ( )10. A. quality ( )11. A. makes ( )12. A. finally ( )13. A. for ( )14. A. forget ( )15. A. position ( )16. A. create ( )17. A. damage ( )18. A. come ( )19. A. drive ( )20. A. quiet | B. sensitive B. joy B. took B. gifts B. special B. time B. different B. normal B. answer B. energy B. gives B. really B. with B. discuss B. relation B. support B. determine B. stop B. hold B. speechless | C. famous C. experience C. returned C. plates C. rare C. hancl C. colorful C. good C. result C. weight C. hides C. especially C. off C. consider C. workmates C. contain C. change C. have C. take C. amazing | D. easy D. stress D. met D. drinks D. delicate D. place D. expensive D. possible D. source D. color D. includes D. nearly D. to D. try D. friends D. own D. increase D. fail D. control D. reasonable |