MATHEMATICS · Multi-part · CBSE · Mathematics · Sequences and Series · Sequences and Series
Problem
Three positive real numbers x,y,z satisfy x+y+z=18.
(i) Show that the product T=xyz is bounded above.
(ii) Prove that the maximum value of T is obtained when the three numbers are equal.
(iii) Determine the maximum value of T and the common value of x,y,z at which it is attained.