2x=1-√5,求x^30-2x^28-x^27
问题描述：
2x=1-√5,求x^30-2x^28-x^27
答
由题得 x^30-2x^28-x^27=x^27(x^3-2x-1)
=x^27(x^3-x^2-X+1-2-X+x^2)
=x^27[(x^3-x^2-X+1)+(x^2--X-2)]
=x^27[(X-1)^2(X+1)+(X+1)(X-2)]
=x^27[(X+1)(X^2-2x+1+X-2)]
=x^27[(X+1)(X^2-x-1)]
=x^27[X^2(X+1)-(x+1)^2]
X=(1-√5)/2 x^2==(1-√5)^2/4=(3--√5)/2
X+1=(3--√5)/2 (x+1)^2=(3-√5)^2/4
x^30-2x^28-x^27 =x^27[X^2(X+1)-(x+1)^2]
=x^27【(3--√5)/2(3--√5)/2- (3-√5)^2/4】
=0