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问题 解答题

已知a1，a2，a3，…a2007，是彼此互不相等的负数，且M=（a1+a2+a3+…+a2006）（a2+a3+…+a2007），N=（a1+a2+a3+…+a2007）（a2+a3+…+a2006），比较M与N的大小．

答案

设a2+a3+…+a2006=k

则M=（a1+k）（k+a2007），N=（a1+k+a2007）×k

M-N=（a1+k）（k+a2007）-（a1+k+a2007）×k

=a1k+a1a2007+k2+ka2007-（a1k+k2+ka2007）

=a1a2007

又由于已知a1，a2，a3，…a2007，是彼此互不相等的负数，a1a2007＞0

M-N=a1a2007＞0

所以M＞N

答：M＞N

单项选择题

Students can learn mathematics only by exploring it on their own, with generous room for trial and error. For what matters in the long run is not acquiring particular computational skills (since without constant use skills rapidly fade), but knowing how to find and use suitable mathematical tools whenever they become necessary.
If the position expressed above is correct, then each of the following can be true EXCEPT:

A．Mathematics teachers are often afraid that someone will ask a question that they cannot answer, and this insecurity frequently leads to authoritarianism in the classroom.

B．Prospective teachers should themselves learn mathematics as a process of constructing and interpreting patterns, of devising strategies for solving problems, and of discovering the beauties and applications of mathematics.

C．Political leaders must accept responsibility for coordinating a nationwide plan for all levels of instruction if mathematics education is to improve.

D．The most effective method for teaching students mathematics is for teachers to state the definitive rule for solving exercises of a given type and then to insist on rote practice in its proper application.

E．(E) Most current teaching presents mathematics as established doctrine, stressing the production of right answers rather than the ability to communicate reasons.
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填空题

一顾客有高度散光且初次配镜，根据配镜原则应用（）。
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