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Question Number 97303 by bobhans last updated on 07/Jun/20

$$\mathbf{G}\mathrm{iven}{\mathrm{x}}_1+{\mathrm{x}}_2+{\mathrm{x}}_3=0,{\mathrm{y}}_1+{\mathrm{y}}_2+{\mathrm{y}}_3=0$$$$\mathrm{and}{\mathrm{x}}_1{\mathrm{y}}_1+{\mathrm{x}}_2{\mathrm{y}}_2+{\mathrm{x}}_3{\mathrm{y}}_3=0.\mathrm{The}\mathrm{value}$$$$\mathrm{of}\frac{{\mathrm{x}}_1^2}{{\mathrm{x}}_1^2+{\mathrm{x}}_2^2+{\mathrm{x}}_3^2}+\frac{{\mathrm{y}}_1^2}{{\mathrm{y}}_1^2+{\mathrm{y}}_2^2+{\mathrm{y}}_3^2}=?$$

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