MATHEMATICS · Multi-part · CBSE · Mathematics · Sequences and Series · Sequences and Series
Problem
Consider two positive real numbers.
(i) Define the arithmetic mean (A.M.) and geometric mean (G.M.) of the two numbers.
(ii) Explain, with algebraic justification, why the arithmetic mean of two positive numbers can never be less than their geometric mean. State the condition for equality.
(iii) Using the result of part (ii), show that when the sum of two positive numbers is fixed, their product is maximised when the two numbers are equal.