Can you solve these equations?

Algebra Level 3

xy+yz= 35yz+xz= 32xz+yx= 27x2+y2+z2= ?\large\begin{aligned}\begin{aligned}xy+yz=&\ 35\\yz+xz=&\ 32\\xz+yx=&\ 27\\x^2+y^2+z^2=&\ ?\end{aligned}\end{aligned}

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