Help with this one please

• carlosego: 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
• aencabo: 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.