# Prove that: #(a+b)/2 = sqrt( a*b)# When #a>=0# and #b>=0# ?

##### 1 Answer

Oct 1, 2017

#### Explanation:

Note that:

#(a-b)^2 >= 0" "# for any real values of#a, b# .

Multiplying out, this becomes:

#a^2-2ab+b^2 >= 0#

Add

#a^2+2ab+b^2 >= 4ab#

Factor the left hand side to get:

#(a+b)^2 >= 4ab#

Since

#a+b >= 2sqrt(ab)#

Divide both sides by

#(a+b)/2 >= sqrt(ab)#

Note that if