#950 · Algebra · Functional equations

Proportionality from cyclic relations

If $a (y + z) = x$ , $b (z + x) = y$ , $c (x + y) = z$ , prove that
$\frac{x ^{2}}{a ( 1 - b c )} = \frac{y ^{2}}{b ( 1 - c a )} = \frac{z ^{2}}{c ( 1 - ab )} .$

~15 minProof · checked by AIcyclic symmetryelimination

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. I. Ratio, Examples I, No. 27

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