An Elegant System of Equations

Algebra Level 2

a+b+c=56a2+b2+c2=1344a2=bcabc= ? \begin{aligned} a+b+c &=& 56 \\ a^2+b^2+c^2 &=& 1344 \\ a^2 &=& bc \\ abc &=& \ ? \\ \end{aligned}

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