Two numbers from two of their means (AM, GM, HM; G^2 = AH): find the numbers or the third mean

This type of question, asked 3 times: CDS 1 2018, CDS 2 2020, CDS 1 2024. All 3 questions below, oldest first.

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Question 1
CDS 1 2018
52 $The arithmetic mean of two numbers is 10 and their geometric mean is 8. What are the two numbers?$
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Question 2
CDS 2 2020
100 $The harmonic mean and the geometric mean of two numbers are 10 and 12 respectively. What is their arithmetic mean ?$
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Question 3
CDS 1 2024
28 $The sum of two positive numbers is 40. If the GM of these two numbers is lower than their AM by 20%, then what is the difference between the two numbers ?$
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Question 1