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下面,仅就阅卷偶得略谈一二。 (一) 学生答卷中不易觉察的错误。题目已知实数a,b,c满足a+b+c=0,abc=8,那么1/a+1/b+1/c的值(A) 是正数; (B) 是零;(C) 是负数; (D) 正、负不能确定。答:( ) 解:由已知可得 b+c=-a,bc=8/a。 s=1/a+1/b+1/c=1/a+(b+c)/(bc)=1/a-a/(bc)=1/a-a~2/8=(8-a~3)/8a。当a=0或a=2,s=0; 当a<0或a>2,s<0; 当00。所以,s的正、负不能确定,应选(D)。此错误颇有迷惑性,求解的过程似乎挑不出什么漏眼,问题出在当0≤a<2时,满足条件a+b+c=0,abc=8的a、b、c不存在。事实上,由于b+c=-a,bc=8/a,则b、c是二次方程
In the following, I have only spoken briefly about reading. (a) Undetectable mistakes in the student’s answer sheet. The topic of known real numbers a, b, c satisfy a+b+c=0, abc=8, then the value of 1/a+1/b+1/c (A) is positive; (B) is zero; (C ) is negative; (D) positive and negative cannot be determined. Answer: () Solution: It is known that b+c=-a and bc=8/a. s=1/a+1/b+1/c=1/a+(b+c)/(bc)=1/aa/(bc)=1/aa~2/8=(8-a~3) /8a. When a=0 or a=2, s=0; when a<0 or a>2, s<0; when 00. Therefore, the positive and negative of s cannot be determined and should be chosen (D). This error is rather confusing. The solution process seems to miss nothing. The problem is that when 0≤a<2, the conditions a+b+c=0 and ab,=abc=8, a, b, and c do not exist. . In fact, since b+c=-a and bc=8/a, b and c are quadratic equations.