Question

If a b c d are in continued proportion then (ad )/(b-c) = x. What is the value of x

Answer 1

let a,b,c,d are a,ar,ar^2,ar^3 respectively such that a,b,c,d are continued proportion then

(a-d)/(b-c)= (a-ar^3)/(ar-ar^2)=(1-r^3)/(r-r^2)= (1+r+r^2)/r = (1/r +r +1)

since (r+ 1/r) is always greater or equal to 2

so, (a-d)/(b-c)= (1/r +r +1) is always greater or equal to 3

so, x=3

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