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已知有理数x满足x²-x+1=0,求（x-1)³+（x-1)²=(x-1)的值错了应该是已知有理数x满足x²-x+1=0，求（x-1)³+（x-1)²+(x-1)的值
题目详情
已知有理数x满足x²-x+1=0,求（x-1)³+（x-1)²=(x-1)的值
错了
应该是
已知有理数x满足x²-x+1=0，求（x-1)³+（x-1)²+(x-1)的值
错了
应该是
已知有理数x满足x²-x+1=0，求（x-1)³+（x-1)²+(x-1)的值
▼优质解答
答案和解析
(x-1)^3+(x-1)^2+(x-1)
=(x-1)[(x-1)^2+(x-1)+1]
=(x-1)[(x^2-2x+1)+x-1+1]
=(x-1)(x^2-2x+1+x-1+1)
=(x-1)(x^2-2x-x+1-1+1)
=(x-1)(x^2-x+1)
=(x-1)x0
=0
=(x-1)[(x-1)^2+(x-1)+1]
=(x-1)[(x^2-2x+1)+x-1+1]
=(x-1)(x^2-2x+1+x-1+1)
=(x-1)(x^2-2x-x+1-1+1)
=(x-1)(x^2-x+1)
=(x-1)x0
=0
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