Question

已知x平方+4x-1=0,求2x的4次方+8x的3次方-4x的平方-8x+1的值是?

如题,求过程及答案

Answer 1

∵x²+4x-1=0
∴x²+4x=1
∴2x^4+8x³-4x²-8x+1
=2x²(x²+4x)-4x²-8x+1
=2x²-4x²-8x+1
=-2x²-8x+1
=-2(x²+4x)+1
=-2+1
=-1