#935 · Algebra · Linear equations

Cyclic Sum Ratio Identity

If $\frac{y + z}{p b + q c} = \frac{z + x}{p c + q a} = \frac{x + y}{p a + q b}$ , shew that $\frac{2 ( x + y + z )}{a + b + c} = \frac{( b + c ) x + ( c + a ) y + ( a + b ) z}{b c + c a + ab}$ .

~15 minProof · checked by AIratiocyclic symmetrylinear systems

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. I. Ratio, Examples I, No. 11

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