The arithmetic mean (A) of two numbers (a and b) is given by the formula A=a+b/2, and their geometric mean (G) is given by G=√ab. Their harmonic mean (H) is given by the formula G= √AH. Which formula correctly gives H in terms of a and b?
A = a+b / 2 G = √( a b ) G = √ ( A H ) / ² ( we will square both sides of the equation ) G² = A H H = G² / 2 [tex]H = \frac{G ^{2} }{A}= \frac{a b}{A}= \\ = \frac{ab}{ \frac{a+b}{2} }= \frac{2ab}{a+b} [/tex]
