Question

let A.M. is the arithmetic mean and G.M. is the geometric mean between a and b; a,b > 0
Which of the following is correct?

a) A.M. >= G.M.
a) A.M. <= G.M.
a) A.M. > G.M.
a) A.M. < G.M.

Answer 1

A.M>G.M

we know,

A.M=  a+b/2                                              G.M.= $\sqrt{ab}$

A.M- G.M= a+b/2 - $\sqrt{ab}$

             =a+b -2$\sqrt{ab}$/2

             =1/2 ($\sqrt{a}$ -$\sqrt{b}$)^2 >0

this is because since it has square so it will always be greater than 0. and thus it will lead to the conclusion arithmetic mean greater than geometric mean.

   A.M> G.M