2. Given that a, b, and c are positive real numbers, show that

Is this true for all real numbers a, b, and c?

3. Show that if a₁, a₂, ..., a_n are positive real numbers, then

4. Let a₁, a₂, ..., a_n-1, a_n be positive, and let a_i, a_j, ..., a_h, a_k be a permutation of these n numbers. Show that 

5. Let a, b, x and y be real numbers, with a² + b² = 1 and x² + y² = 1. Show that:

(a) 

(b) 

(c) 

(d) 
 
 

Monday, June 22, 1998