已知实数x满足x^2+1/(x^2)+x-1/x=4,则4-1/x的值是（ ）A.-2 B.1 C.-1或2 D.-2或1谢

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已知实数x满足x^2+1/(x^2)+x-1/x=4,则4-1/x的值是（ ）A.-2 B.1 C.-1或2 D.-2或1谢

已知实数x满足x^2+1/(x^2)+x-1/x=4,则4-1/x的值是（ ）A.-2 B.1 C.-1或2 D.-2或1谢
已知实数x满足x^2+1/(x^2)+x-1/x=4,则4-1/x的值是（ ）
A.-2 B.1 C.-1或2 D.-2或1
谢

已知实数x满足x^2+1/(x^2)+x-1/x=4,则4-1/x的值是（ ）A.-2 B.1 C.-1或2 D.-2或1谢
(x-1/x)² = x² + 1/x² - 2
所以 x² + 1/x² = (x-1/x)² + 2
所以原式= (x-1/x)² + 2 + x - 1/x = 4
设 x-1/x = a
则 a²+a - 2 = 0
解得 a = -2 或者 a =1.
所以 x-1/x = -2 或者 x-1/x = 1
从结果来看,你抄题抄错了,选D.

x^2+1/(x^2)+x-1/x=4
x²-2x*（1/x）+1/x² + x-1/x -2=0
（x-1/x）²+（x-1/x）-2=0
将x-1/x看成一个未知数，解得：
x-1/x=-2或x-1/x=1
选D。

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