若x=(1-√5)/2,则√(1/x-1/x³)-³√(x^4-x²)的值为A 1/2 B 1 C √5/2 D√5

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若x=(1-√5)/2,则√(1/x-1/x³)-³√(x^4-x²)的值为A 1/2 B 1 C √5/2 D√5

若x=(1-√5)/2,则√(1/x-1/x³)-³√(x^4-x²)的值为A 1/2 B 1 C √5/2 D√5
若x=(1-√5)/2,则√(1/x-1/x³)-³√(x^4-x²)的值为
A 1/2 B 1 C √5/2 D√5

若x=(1-√5)/2,则√(1/x-1/x³)-³√(x^4-x²)的值为A 1/2 B 1 C √5/2 D√5
x=(1-√5)/2 < 0
===> x^2 = (3-√5)/2
===> x^2-1 = x
因此:
√(1/x-1/x³)-³√(x^4-x²)
=√[ (x^2-1)/x³] - ³√ [ x^2(x^2-1) ]
=√[1/x^2] - ³√ [ x^3 ]
=-1/x-x
=(1+√5)/2 - (1-√5)/2
=√5

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