已知:x=2-根号5,则x^4-8x^3+16x^2-x+1=

题目

已知:x=2-根号5,则x^4-8x^3+16x^2-x+1=

答案

x=2-√5,x-2=-√5.x^4-8x^3+16x^2-x+1 =(x^4-4x^3+4x^2)-4x^3+12x^2-x+1 =x^2(x-2)^2-4x^3+12x^2-x+1 =5x^2-4x^3+12x^2-x+1 =-4x^3+17x^2-x+1 =-4x^3+16x^2-16x+x^2+15x+1 =-4x(x-2)^2+x^2+15x+1 =-20x+x^2+15x+1 =x...