椭圆x²/a²+y²/b²=1(a>b>0)上一点A关于原点的对称点为B,F为其右焦点,若AF⊥BF,设∠ABF=α,且α∈(π/12,π/4],求该椭圆离心率的取值范围.
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![椭圆x²/a²+y²/b²=1(a>b>0)上一点A关于原点的对称点为B,F为其右焦点,若AF⊥BF,设∠ABF=α,且α∈(π/12,π/4],求该椭圆离心率的取值范围.](/uploads/image/z/1470527-71-7.jpg?t=%E6%A4%AD%E5%9C%86x%26sup2%3B%2Fa%26sup2%3B%2By%26sup2%3B%2Fb%26sup2%3B%3D1%28a%EF%BC%9Eb%EF%BC%9E0%29%E4%B8%8A%E4%B8%80%E7%82%B9A%E5%85%B3%E4%BA%8E%E5%8E%9F%E7%82%B9%E7%9A%84%E5%AF%B9%E7%A7%B0%E7%82%B9%E4%B8%BAB%2CF%E4%B8%BA%E5%85%B6%E5%8F%B3%E7%84%A6%E7%82%B9%2C%E8%8B%A5AF%E2%8A%A5BF%2C%E8%AE%BE%E2%88%A0ABF%3D%CE%B1%2C%E4%B8%94%CE%B1%E2%88%88%EF%BC%88%CF%80%2F12%2C%CF%80%2F4%5D%2C%E6%B1%82%E8%AF%A5%E6%A4%AD%E5%9C%86%E7%A6%BB%E5%BF%83%E7%8E%87%E7%9A%84%E5%8F%96%E5%80%BC%E8%8C%83%E5%9B%B4.)
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