So High Yet So Low

\(A\) and \(B\) are points at a distance \(h\) from the surface of the earth where the value of the acceleration due to gravity is the same. \(A\) is above the surface and \(B\) is below the surface.

If \(h=\left( \dfrac{ \sqrt{k}-1}{2}\right)R\), where \(R\) is the radius of the Earth, compute \(k\).

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