椭圆x^2/a^2+y^2/b^2=1(a>b>0)与直线x+y=1交于P,Q两点,且OQ垂直OP,其中O为坐标原点(1)求1/a^2+1/b^2的值(2)若椭圆的离心率e满足3分之根号三≤e≤二分之根号2,求椭圆长轴的取值范围
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![椭圆x^2/a^2+y^2/b^2=1(a>b>0)与直线x+y=1交于P,Q两点,且OQ垂直OP,其中O为坐标原点(1)求1/a^2+1/b^2的值(2)若椭圆的离心率e满足3分之根号三≤e≤二分之根号2,求椭圆长轴的取值范围](/uploads/image/z/4337110-46-0.jpg?t=%E6%A4%AD%E5%9C%86x%5E2%2Fa%5E2%2By%5E2%2Fb%5E2%3D1%28a%3Eb%3E0%29%E4%B8%8E%E7%9B%B4%E7%BA%BFx%2By%3D1%E4%BA%A4%E4%BA%8EP%2CQ%E4%B8%A4%E7%82%B9%2C%E4%B8%94OQ%E5%9E%82%E7%9B%B4OP%2C%E5%85%B6%E4%B8%ADO%E4%B8%BA%E5%9D%90%E6%A0%87%E5%8E%9F%E7%82%B9%EF%BC%881%EF%BC%89%E6%B1%821%2Fa%5E2%2B1%2Fb%5E2%E7%9A%84%E5%80%BC%EF%BC%882%EF%BC%89%E8%8B%A5%E6%A4%AD%E5%9C%86%E7%9A%84%E7%A6%BB%E5%BF%83%E7%8E%87e%E6%BB%A1%E8%B6%B33%E5%88%86%E4%B9%8B%E6%A0%B9%E5%8F%B7%E4%B8%89%E2%89%A4e%E2%89%A4%E4%BA%8C%E5%88%86%E4%B9%8B%E6%A0%B9%E5%8F%B72%2C%E6%B1%82%E6%A4%AD%E5%9C%86%E9%95%BF%E8%BD%B4%E7%9A%84%E5%8F%96%E5%80%BC%E8%8C%83%E5%9B%B4)
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