Question

Help with this one please

Answer 1

The correct answer is the first option, which is:

 A=G^2/H; H=G^2/A

 The explanation is shown below:

 1. To solve the exercise shown in the figure attached, you must apply the proccedure shown below:

 2. You have the following equation to calculate G:

 G=√AH

 3. Now, to find the formula to calculate A, you must clear the A, as below:

 G^2=(√AH)^2
 G^2=AH
 A=G^2/H

 4. Then, you must apply the same proccedure to find the formula for calculate H, as following:

 G^2=(√AH)^2
 G^2=AH
 H=G^2/A

Answer 2

Since we are given by G=sqrt(AH):

Rewriting;
G=sqrt(AH)
//square both sides//
G^2=[sqrt(AH)]^2
G^2=AH
A=G^2/H

G=sqrt(AH)
//square both sides//
G^2=[sqrt(AH)]^2
G^2=AH
H=G^2/A

Thus, the answer is the first option which has A=G^2/H and H=G^2/A

The Root-Mean Square-Arithmetic Mean-Geometric Mean-Harmonic Mean Inequality (RMS-AM-GM-HM), is an inequality of the root-mean square, arithmetic mean, geometric mean, and harmonic mean of a set of positive real numbers  that says:

with equality if and only if . This inequality can be expanded to the power mean inequality.

As a consequence we can have the following inequality: If  are positive reals, then  with equality if and only if ; which follows directly by cross multiplication from the AM-HM inequality.This is extremely useful in problem solving.