(a^2-1)x+1≥ [(a-1)x+1]^2(a≠1)

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(a^2-1)x+1≥ [(a-1)x+1]^2(a≠1)
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(a^2-1)x+1≥ [(a-1)x+1]^2(a≠1)
(a^2-1)x+1≥ [(a-1)x+1]^2(a≠1)

(a^2-1)x+1≥ [(a-1)x+1]^2(a≠1)
(a^2-1)x+1>=(a-1)^2x^2+2(a-1)x+1
(a-1)^2x^2-(a^2-2a+1)x<=0
(a-1)^2x^2-(a-1)^2x<=0
(a-1)^2(x^2-x)<=0
x^2-x<=0
x(x-1)<=0
x<=0且x>=1无解
x>=0且x<=1,即:0<=x<=1
不等式的解为[0,1]

(a²-1)x+1>=(a-1)²x²+2(a-1)x+1
(a-1)²x²+[2(a-1)-(a²-1)]x<=0
(a-1)²x²-(a-1)²x<=0
a≠1则(a-1)²>0
两边除以(a-1)²
x²-x≤0
x(x-1)≤0
0≤x≤1