Past exam of the mathematics course of the University of Cambridge / 2022 / ia / Paper 1 / 1B / a / i

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- Solution i

Solution

The triangle inequality gives

∣ a - b ∣ = ∣ (a - z) + (z - b) ∣ \leq ∣ z - a ∣ + ∣ z - b ∣.

Hence the left-hand side of the proposed equation is always at least $∣ a - b ∣$ . There are no solutions when $c < ∣ a - b ∣$ .

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