Mathematics I - Old Questions
Question Answer Details
10. a) If arithmetic mean, geometric mean and harmonic mean between two unequal positive numbers are A, G, H respectively. Then prove that A > G > H. (4)
Answer
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Official Answer
Let and be two real positive and unequal numbers and let be arithmetic, geometric and harmonic mean respectively then,
A = 
G = 
H = 
Now,
A - G =
A - G > 0 i.e. A>G
Again,
G - H = 
G - H > 0 i.e. G>H
Hence proved that
A > G > H