Problem #PRU-61174

Problem

The positive real numbers $a, b, c, x, y$ satisfy the following system of equations: ${\begin{array}{r} x^{2} + x y + y^{2} = a^{2} \\ y^{2} + y z + z^{2} = b^{2} \\ x^{2} + x z + z^{2} = c^{2} \end{array}$

Find the value of $x y + y z + x z$ in terms of $a, b,$ and $c .$

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