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For two positive real numbers, how does the arithmetic mean compare with the geometric mean?
AA is smaller or equal
BA is always smaller
CA is always unequal
DA is greater or equal
Answer & Solution
Correct answer: D. A is greater or equal
1. Write A for the arithmetic mean and G for the geometric mean.
2. Their difference works out to a square divided by two.
3. A square is never negative, so that difference is never negative.
4. From this we obtain the relationship A is greater than or equal to G.
_Source: NCERT Class XI Mathematics, Ch 8 'Sequences and Series'_
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