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Symmetric sums of three variables · Algebra · Earlier days

Pairwise products from a symmetric system

Let x,y,zx, y, z be positive numbers satisfying the system x2+xy+y2=108x^{2}+xy+y^{2}=108, y2+yz+z2=16y^{2}+yz+z^{2}=16, z2+xz+x2=124z^{2}+xz+x^{2}=124. Find the value of xy+yz+xzxy+yz+xz.

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