#1048 · Algebra · Sequences & series

Ratio from means

If the harmonic mean of two quantities is to their geometric mean as $12$ is to $13$ , prove that the quantities are in the ratio $4$ to $9$ .

~6 minProof · checked by AIHarmonic meanGeometric meanRatio

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. VI. Harmonical Progression, Examples VI.a, No. 5

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.