如果x=1/根号2-1,求x^5-2x^4-x^3-4x^2+8x+2016的值

题目

如果x=1/根号2-1,求x^5-2x^4-x^3-4x^2+8x+2016的值

答案

x=1/根号2-1
x=√2+1
x^5-2x^4-x^3-4x^2+8x+2016
=x^3（x^2-2x-1）-4（x^2-2x）+2016
=（√2+1)^3(2+2√2+1-2√2-2-1)-4(2+2√2+1-2√2-2)+2016
=-4+2016
=2012