Question

已知X2-2x-1=0,求X4-5X3+11X2-9x-5的值。

注；在字母后的书为几次方指数。要用多项式除法应用。（高中）
答案是1啊。

Answer 1

已知X2-2x-1=0,
X4-5X3+11X2-9x-5
=X4-2X3-x2-3x3+12X2-9x-5
=X²(X²-2X-1)-(3x³-6X²-3x)+6X²-12x-5
=X²(X²-2X-1)-3X(x²-2X-1)+(6X²-12x-6)+1
=X²(X²-2X-1)-3X(x²-2X-1)+6(X²-2X-1)+1---------------------------(已知 X²-2X-1=0,)
=1