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 ofa, 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