Question

if 1/2y is the A.M. between 1/y-x and 1/y-z, prove that y is the G.M. between xand z.​

Answer 1

Answer:

Step-by-step explanation:

ok see,

if 1/2y is a arithmetic mean between 1/y-x and 1/y-z then ,

1/2y=(1/y-x  +   1/y-z)/2

so,

y^2-2y-xy+xz  = 2y^2 -xy -xz   on simplification

so on cancelling terms we get

y^2=xz

or y/x=z/y

this proves x,y,z are in GP and y is the GM between x and y

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