An algebra problem by Phudish Prateepamornkul

Algebra Level 4

If $$x^2-yz-zw-wy=116$$ , $$y^2-zw-wx-xz=117$$ , $$z^2 - wx - xy - yw = 130$$ and $$w^2 - xy - yz - zx = 134$$, then find the value of $$x^2 + y^2 + z^2 +w^2$$.

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