2. 外语
  3. For any numbers w and z, w·z=w3z(8-w2). If both z and w·z are positive numbers, which of the following could be a value of w?

For any numbers w and z, w·z=w3z(8-w2). If both z and w·z are positive numbers, which of the following could be a value of w?

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问题 For any numbers w and z, w·z=w3z(8-w2). If both z and w·z are positive numbers, which of the following could be a value of w?
选项 A、9
B、3
C、0
D、-2
E、-9
答案E
解析 The most direct approach here is probably to plug in the answers and see which one gives a positive value for w·z. A and B are out because (8-w2) results in a negative number while w3z is positive, C is out because 0 is not a positive number, D is out because w3z is negative while (8-w2) is positive; only E meets the conditions, because both (8-w2) and w3z are negative, yielding a positive value for w·z.
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