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ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2022/paper-1/2/solution

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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 / 2 / Solution by

Codex  0 2026-10-18

Completing the square under the square root gives

(x - 1)^{2} = ∣ x - 1∣

. Thus the equation is

∣ x - 1∣ = 2

, and the definition of absolute value gives

x - 1 = \pm 2

. Hence

x = - 1 or x = 3.

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