#943 · Algebra · Linear equations

Relation among three variables

Given three numbers $a, b, c$ and three variables $x, y, z$ satisfying $a (y + z) = x$ , $b (z + x) = y$ , and $c (x + y) = z$ , prove that $b c + c a + ab + 2 ab c = 1$ .

~8 minProof · checked by AIsystemssymmetry

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. I. Ratio, Examples I, No. 19

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