Question

已知有理数x满足x的平方-x+1=0,求（x-1）的三次方+（x-1）的二次方+（x-1)的值.

Answer 1

用中文二代表二次方中文三代表三次方,

已知:X二-X+1=0 ①

开始求:(X-1)三+(X-1)二+(X-1)

把上式化为:

(X-1)[(X-1)二+(X-1)+1]

再化简为:

(X-1)[X二-2X+1+X-1+1]

再化一次:

(X-1)(X二-X+1)

把①式代入.得

(X-1)?0

结果:答案为0