x∈(-1,1)恒成立,2x²+(a-1)x-a(a-1)
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x∈(-1,1)恒成立,2x²+(a-1)x-a(a-1)
x∈(-1,1)恒成立,2x²+(a-1)x-a(a-1)
x∈(-1,1)恒成立,2x²+(a-1)x-a(a-1)
y=2x^2+(a-1)x-a*(a-1)为开口向上的抛物线,由韦达定理得
x1+x2=-(a-1)/2
x1x2=-a(a-1)/2
(1)a=1,顶点在(0,0),显然是不符合要求
(2)a>1时,对称轴在x=-(a-1)/41即满足题意
x2=1时,x1=-(a-1)/2-1=-(a+1)/2
x1x2=-(a+1)/2 = -a(a-1)/2
a+1=a^2-a
a^2-2a-1=0
a=1+-V2 取正解 1+V2
a>1+V2
(2)a0处,只要左解x1