已知X=1-根号3,求x5-2x4-2x3-2x+x2-1的值.
问题描述：
已知X=1-根号3,求x5-2x4-2x3-2x+x2-1的值.
答
x5-2x4-3x3+x2-2x-3.=x^3(x^2-2x-3)+(x^2-2x-3) =(x^3+1)(x^2-2x-3) =(x+1)(x^2-x+1)(x+1)(x-3) =(x+1)^2(x^2-x+1)(x-3) 已知X=1-根号3 所以(x-1)^2=3 x^2-2x-2=0 x^2-x+1=x+3 (x+1)^2=3+4x,x^2-9=2x-7=(x+1)^2(x-3)...