If x is the harmonic mean between y and z, then which one of the following is correct ?

Given:

x is the harmonic mean between y and z.

Concept:

Harmonic mean (HM):  If a, b & c are in AP then,

1/a, 1/b, 1/c are in harmonic progression (HP). 

If H is the harmonic mean of a & b, then

H = \(\frac{2}{\frac{1}{a} \ + \ \frac{1}{b} }\) or H = \(\frac{2ab}{a\ + \ b}\)

Calculation:

We have,

x is the harmonic mean of y and z

⇒ x = \(\frac{2yz}{y \ + \ z}\)

⇒ xy + xz = 2yz

⇒ xy + xz - 2yz = 0

∴ If x is the harmonic mean between y and z, then xy + xz - 2yz = 0.