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HKIMO 2026 THPT (Grades 10–12 shared) National Final (Heat) Set 05 Question 15

HKIMO · HKIMO 2026 THPT (Grades 10–12 shared) National Final (Heat) Set 05

Question 15

Both $a$ and $\sqrt{23-8\sqrt7}+a\sqrt{23+8\sqrt7}$ are rational. Find $a$.