论文部分内容阅读
在初中数学竞赛中,常出现一类代数式求值问题,如: (1) 已知x=2-3~(1/2),求x~4-5x~3+6x~2+5x的值。(1986年上海市初中数学竞赛试题) (2) 若x=(5~(1/2)-1)/2,则x~4+x~2+2x-1=____。(第六届全国部分省市初中数学通讯赛试题) (3) 已知x=(111~(1/2)-1)/2,求多项式(2x~5+2x~4-53x~3-57x+54)~(1989)值。(1989年浙江省初中二年级数学竞赛试题) (4) 已知a=(22~(1/2)+5~(1/2))/(5~(1/2)-2~(1/2))求值:a~5-7a~4+6a~3-7a~2+11a+13。(第三届求是杯数学竞赛初二试题) (5) 当x=3~(1/2)-1时,代数式 (x+4)/(x~3+6x~2+5x-3~(1/2)-15)的值是多少?(88—89学年度广州、福州、武
In the junior high school math competition, there is often a problem of algebraic type evaluation, such as: (1) Known x=2-3~(1/2), find the value of x~4-5x~3+6x~2+5x . (1986 Shanghai Junior High School Mathematics Contest) (2) If x=(5~(1/2)-1)/2, then x~4+x~2+2x-1=____. (Questionnaires for the 6th National Junior School Mathematical Communication Competition) (3) Knowing x=(111~(1/2)-1)/2 to find polynomials (2x~5+2x~4-53x~3- 57x+54)~(1989) values. (1989 Zhejiang Provincial Junior High School Mathematics Competition Question) (4) Known a=(22~(1/2)+5~(1/2))/(5~(1/2)-2~(1) /2)) Evaluation: a~5-7a~4+6a~3-7a~2+11a+13. (The 3rd Mathematical Competition Mathematical Competition Test 2) (5) When x=3~(1/2)-1, algebraic expression (x+4)/(x~3+6x~2+5x-3~ What is the value of (1/2)-15)? (Year 88-89 Guangzhou, Fuzhou, Wu