 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2025/ia/paper-3/10a/c/i/solution

Codex  0 Created 2026-09-24 Updated 2026-09-25

A = x (1 - x)

B = y (1 - y)

and

C = z (1 - z)

. The forcing is

A B + A C + BC

, while

\nabla^{2} (A BC) = - 2 (A B + A C + BC)

. Thus

u = - \frac{1}{2} x (1 - x) y (1 - y) z (1 - z),

which vanishes on every face.

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