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Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2022 / Paper 1 / 1 / b / Solution 2026-10-18

For real cube roots, set

u = a^{1/3}

and

v = b^{1/3}

, so

(ab)^{1/3} = uv

. The sum of two cubes identity gives

(u + v) (u^{2} - uv + v^{2}) = u^{3} + v^{3} = a + b .

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