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解方程:(x-1)(x+1)(x2+1)=(x-1)(x+1)(x2+1)(x4+1)(x8+1).

题目详情
解方程:(x-1)(x+1)(x2+1)=(x-1)(x+1)(x2+1)(x4+1)(x8+1).
▼优质解答
答案和解析
(x-1)(x+1)(x2+1)=(x-1)(x+1)(x2+1)(x4+1)(x8+1),
x4-1=x16-1,
x16-x4=0,
x4(x6+1)(x6-1)=0,
x4=0,x6+1=0(无解),x6-1=0,
x1=0,x2=-1,x3=-1.