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Gaokao Math Practice Question

已知函数 $f(x)=x^{2}-2 x+a\left(e^{x-1}+e^{-x+1}\right)$ 有唯一零点, 则 $a=(\qquad)$

  1. A.$-\frac{1}{2}$
  2. B.$\frac{1}{3}$
  3. C.$\frac{1}{2}$
  4. D.1

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