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标题: jj question [打印本页]

作者: assfgrtrtr 时间: 2004-7-6 10:25 标题: jj question

this is from last May:fficeffice" />

24． X^2 + 1/(X^2) = 1 X^4 + 1/(X^4) = ? [确认]：-1

"-1"? how is that possible?

作者: nbnhjf 时间: 2004-7-6 10:48

X^4 + 1/(X^4) => { X^2 + 1/(X^2)} ^2 - 2 * X^2 * 1/(X^2) = 1-2 = -1fficeffice" />

作者: llllyyyy 时间: 2004-7-12 11:01

Yes, the calculation is right, but I think it is impossible. Because x^4 must >=0 and 1/x^4 also must >=0

Can anyone explain this for me? Thanks a lot.

作者: smart 时间: 2004-7-12 17:28

X^2 + 1/(X^2) = 1这个条件给的就有问题。
由X^2 + 1/(X^2) = 1=> X^4 -X^2 + 1＝0，其判别式小于0，也就是说X在实数范围内没有根。所以才能导致在解题后X^4 + 1/(X^4) =－1小于0的结果。

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