如果x^2-2x-1=0,求x^4+x^3-5x^2-7x+5的值.

问题描述:

如果x^2-2x-1=0,求x^4+x^3-5x^2-7x+5的值.

x²=2x+1
则以下x²用2x+1代替
x³=x(x²)
=x(2x+1)
=2x²+x
=2(2x+1)+x
=5x+2
x^4=(x²)²
=(2x+1)²
=4x²+4x+1
=4(2x+1)+4x+1
=12x+5
原式=(12x+5)+(5x+2)-5(2x+1)-7x+5
=12x+5x+2-10x-5-7x+5
=2