If \( a=8+3 \sqrt{7} \) and \( b=\frac{1}{a} \), what will be the value of \( a^{2}+b^{2} \) ?

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If \( a=8+3 \sqrt{7} \) and \( b=\frac{1}{a} \), what will be the value of \( a^{2}+b^{2} \) ?
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