Solve it either Geometrically or Algebraically

Geometry Level 4

Let \({ a }_{ k }, { b }_{ k }, l \in { \Re }^{ + }\) and \({ a }_{ k }^{ 2 }+{ b }_{ k }^{ 2 } = { l }^{ 2 }\)

\(E = \cfrac { { a }_{ k }{ b }_{ k } }{ { a }_{ k }^{ 2 }+{ b }_{ k }^{ 2 }+({ a }_{ k }+{ b }_{ k })\sqrt { { a }_{ k }^{ 2 }+{ b }_{ k }^{ 2 } } }\)

Find maximum value of \(E\)

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