Systems of equations

Algebra Level 4

{y2+u2+v2+w2=4x1x2+u2+v2+w2=4y1x2+y2+v2+w2=4u1x2+y2+u2+w2=4v1x2+y2+u2+v2=4w1 \begin{cases} y^2 + u^2 + v^2 + w^2 = 4x - 1 \\ x^2 + u^2 + v^2 + w^2 = 4y - 1 \\ x^2 + y^2 + v^2 + w^2 = 4u - 1 \\ x^2 + y^2 + u^2 + w^2 = 4v - 1 \\ x^2 + y^2 + u^2 + v^2 = 4w - 1 \\ \end{cases}

If y,u,v,wy,u,v,w and xx are real numbers satisfying the systems of equations above, find y+u+v+w+xy+u+v+w+x.

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