#1902 · Algebra · Systems

Symmetric Equal Products

If $x (2 a - y) = y (2 a - z) = z (2 a - u) = u (2 a - x) = b^{2}$ , shew that $x = y = z = u$ unless $b^{2} = 2 a^{2}$ , and that if this condition is satisfied the equations are not independent.

~25 minProof · checked by AIsystems of equationssymmetry

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Miscellaneous Examples, No. 297

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