Answer to Question #44532 in Algebra for JASHVINDER

Question

Given a, b > 0 such that ab = 18, check whether their sum is greatest when a = b.

Answer 1

If ab=18 and a=b, then a²=18. Hence, a=sqrt(18)=3sqrt(2), because a>0. From inequality of arithmetic and geometric means a+b>=2sqrt(ab)=2sqrt(18)=6sqrt(2) and equality sign will be in case of a=b, but this case corresponds to the minimal value of a+b.