Solve it either Geometrically or Algebraically

Geometry Level 5

Let ak,bk,l+{ a }_{ k }, { b }_{ k }, l \in { \Re }^{ + } and ak2+bk2=l2{ a }_{ k }^{ 2 }+{ b }_{ k }^{ 2 } = { l }^{ 2 }

E=akbkak2+bk2+(ak+bk)ak2+bk2E = \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 EE

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