Question
Download Solution PDFIf a, b, c are the positive integers, then (a + b)(b + c)(c + a) is
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
If a,b,c are the positive integers, then
1. Arithmetic mean:
2. Geometric mean
3. Harmonic mean
4. The relation between AM, GM, and HM
- G2 = AH
- AM ≥ GM ≥ HM
Calculation:
We know that,
AM ≥ GM
⇒
Similarly,
Multiplying these inequalities, we will get
⇒ (a + b)(b + c)(c + a) ≥ 8abc
Hence, ≥ 8abc is the correct answer.
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