Arithmetic Mean

[greatwhiteshark]

If a < b, show that a < (a+b)/2 < b. The number (a+b)/2 is called the arithmetic mean of a and b.

 

[Denis]

d = b - a; then:
a = b - d [1]
b = a + d [2]

[1] (a+b) / 2 = (b - d + b) / 2 = (2b - d) / 2 < b

[2] (a+b) / 2 = (a + a + d) / 2 = (2a + d) / 2 > a

 

[pka]

This ia another way.

 

[greatwhiteshark]

Two Ways

I like the two different methods of solving this question.

 

[~Midnight.Kitten~]

is that like..simplifying expressions?

 

[Guest]

is that like..simplifying expressions?

The task is to prove what the problem statement said to prove. You simplify whatever you can along the way to make it look nice.