#933 · Algebra · Linear equations

Continued Proportion Identity

If $\frac{a}{b} = \frac{b}{c} = \frac{c}{d}$ , prove that $\frac{a}{d}$ is equal to $\frac{a ^{5} + b ^{2} c ^{2} + a ^{3} c ^{2}}{b ^{4} c + d ^{4} + b ^{2} c d ^{2}}$ .

~10 minProof · checked by AIcontinued proportionalgebraic manipulationradicals

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. I. Ratio, Examples I, No. 8

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