已知x²+4x-1=0,求2x⁴+8x³-4x²-8x+1的值.

问题描述:

已知x²+4x-1=0,求2x⁴+8x³-4x²-8x+1的值.

2x⁴+8x³-4x²-8x+1
=2x(x²+4x-1)-(2x²+8x-1)
=2x²(x²+4x-1)-(2x²+8x-2)-1
=2x²(x²+4x-1)-2(x²+4x-1)-1
=-1