已知x²+4x-1=0,求2x^4+8x³-4x²-8x+1的值

已知x²+4x-1=0,求2x^4+8x³-4x²-8x+1的值
已知x²+4x-1=0,求2x^4+8x³-4x²-8x+1的值

已知x²+4x-1=0,求2x^4+8x³-4x²-8x+1的值
2x^4+8x³-4x²-8x+1
=2x²(x²+4x)-4(x²+2x)+1
=2x²(x²+4x-1)-4(x²+4x-1)+2x²+8x-4+1 (注：x²+4x-1=0)
=2x²+8x-3
=2（x²+4x-1）+2-3
= -1

-1