Prove that the A.M. of two positive real numbers is greater than their G.M.

Answer

N/a

Explanation

Let a and b two positive real numbers of their A.M. `"So the ratio of numbers "=(2+sqrt(3)):(2-sqrt(3)).`
`"Now, "A-G=(a+b)/(2)-sqrt(ab)=(a+b-2sqrt(ab))/(2)=((sqrt(a)-sqrt(b))^(2))/(2)gt0`
`rArr" "A-Ggt0`
`rArr" "AgtG`
Therefore, the A.M. of two positive real numbers is greater than their G.M.