#966 · Algebra · Linear equations

Continued proportion identity

If $a, b, c, d, e$ are in continued proportion (i.e. $a : b = b : c = c : d = d : e$ ), prove that $(ab + b c + c d + d e)^{2} = (a^{2} + b^{2} + c^{2} + d^{2}) (b^{2} + c^{2} + d^{2} + e^{2}) .$

~10 minProof · checked by AIContinued proportionAlgebraic identities

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. II. Proportion, Examples II, No. 17

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