Prove that A. M, G. M. and H. M between any two unequal positive numbers satisfy the following relations. i. (G. M)²= (A. M)×(H. M)
ii. A.M>G. M>H. M​

See below

Step-by-step explanation:

we want to prove that A.M, G.M. and H.M between any two unequal positive numbers satisfy the following relations.

well, to do so let the two unequal positive numbers be where:

the AM,GM and HM of and is given by the following table:

simplify addition:

reduce fraction:

simplify complex fraction:

reduce fraction:

rewrite:

hence, PROVEN

square root both sides:

isolate right hand side expression to left hand side and change its sign:

square both sides:

expand using (a-b)²=a²-2ab+b²:

move -2√x_1√x_2 to right hand side and change its sign:

divide both sides by 2:

again,

expand:

move the middle expression to right hand side and change its sign:

cross multiplication:

hence,

PROVEN

x

step-by-step explanation: