Selected Sample Problems and Solutions
Problem 1: If a, b, c are three positive real numbers such that , then find the maximum value of the expression ?
Solution: Use inequality on to get the answer as 27 .
Problem 2: In problem 1, find the minimum value of ?
Solution: Use inequality on to get the answer as 12 . [QM and AM stand for quadratic and arithmetic means respectively].
Problem 3: Find the value of the limit
Solution: . Detailed solution
Problem 4: Find the value of the limit
Solution: 1. Detailed solution
Problem 5: If is a real number and , find the value of ?
Solution: 1/2 . Detailed solution
Problem 6: Find the minimum value of the below expression for all real values of ?
Problem 7 : For positive real numbers a, b, x such that and show that