#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

Stuck? A gentle nudge

Something off?

Workspace

Your working

Check your full solution

Attach photos of your pages (up to 3) or one PDF — or check what you typed above. Lemma reads the work and verifies the reasoning, not just the answer.

Your first check today doesn't need an account.

Your photos and PDFs are read once and not stored — only the transcription is kept.