Am, Gm, Hm Relations
For two positive numbers a and b, which of the following is always true?
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About This Question
- Subject
- mathematics
- Chapter
- sequence and series
- Topic
- am, gm, hm relations
- Difficulty
- Easy
- Year
- 2025
Solution
Correct Answer:
AM ≥ GM ≥ HM
- Definition of Inequalities: For any positive real numbers:
- Arithmetic Mean (AM) =(a+b)/2
- Geometric Mean (GM) =ab
- Harmonic Mean (HM) =2ab/(a+b)
- Relation: It is a fundamental theorem that AM≥GM≥HM.
- Equality: Equality (AM=GM=HM) holds if and only if a=b.
- Validation: Test 2 and 8: AM=5, GM=4, HM=3.2. 5>4>3.2 (True).
This easy difficulty mathematics question is from the chapter sequence and series, covering the topic of am, gm, hm relations. It appeared in the 2025 exam.
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