Given that \(\displaystyle\sum _{ n=1 }^{ k }{ { x }_{ n }^{ 2 } } =9\) and that \(\displaystyle\sum _{ n=1 }^{ k }{ { y }_{ n }^{ 2 } } =5329\)

Find the maximum value of \(\displaystyle\sum _{ n=1 }^{ k }{ { ({ x }_{ n }+{ y }_{ n }) }^{ 2 } } \).

**Note**: \({x}_{n},{y}_{n}\ge0\).

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