Side Squared

Geometry Level 4

\(ABCD\) is a quadrilateral where \(AB=AD=CD=l\). \(\triangle BCD\) is right, and \(\triangle ABD\) is isosceles. It is given that \(BC=\color{#03D300}{X}=l^2\). By considering \(\color{blue}{\alpha}\), or otherwise, find the set of all possible values of \(\color{#03D300}{X}\).

Input \(a+b\) as your answer, where \(a<\color{#03D300}{X}<b\).

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