Question

If x be the A.M. between y and z, y the G.M. between z and x, prove that z be the H.M. between x and y.

Answer 1

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Answer 2

Answer:

x=(y+z)/2.....eqn i

y^2=xz

now,

multiplying by y in eqn i

so, xy=(y^2+zy)/2

2xy= xz+zy (y^2=xz)

2xy= z(x+y) taking z common

z = 2xy/(x+y)

proved