Proportion radical identity

If $a : b = c : d$ , prove that $a^{2} + c^{2} : b^{2} + d^{2} = a c + \frac{c ^{3}}{a} : b d + \frac{d ^{3}}{b}$ .

~10 minProof · checked by AIproportionsratios

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. II. Proportion, Examples II, No. 7

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