# If H is the harmonic mean between P and Q then the values of (H/P)+(HQ) is equal to ?

##### 1 Answer

Sep 27, 2017

# H/P + HQ = 2P #

#### Explanation:

In general, the harmonic mean is given by:

# mu_H = n/(sum_(r=1)^(n) 1/x_(i) ) #

So for the two numbers

# H = 2/(1/P+1/Q) #

And if we use a common denominator, we can simplify:

# H = 2/( (Q+P)/(PQ) ) = (2PQ) / (P+Q ) # ..... [A]

So the we seek:

# H/P + HQ = H (1/P + Q )#

# " " = H ( (Q+P)/Q )#

# " " = ( (2PQ) / (P+Q ) ) ( (Q+P)/Q ) \ \ \ \ # using [A]

# " " = 2P #