已知x2+4x-1=0,则2x4+8x3-4x2-8x+1的值是多少?

已知x²+4x-1=0,则2x⁴+8x³-4x²-8x+1的值是多少?

答案

-1.

提示：利用整体代换来降幂简便.∵x²+4x=1,∴2x⁴+8x³-4x²-8x+1=2x²(x²+4x)-4x²-8x+1=2x²- 4x²-8x+1=-2x²-8x+1=-2(x²+4x)+1=-2+1=-1.

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已知x2+4x-1=0,则2x4+8x3-4x2-8x+1的值是多少?

答案

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