- #1

utkarshakash

Gold Member

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## Homework Statement

Let a,b,c be in G.P. and a-b,c-a,b-c in H.P. If both roots of [itex](a+c)x^2 + bx + 4b^2=0[/itex] are positive and minimum value of 'b' be k then value of |[k]|

## Homework Equations

## The Attempt at a Solution

Let a,b,c be denoted by a,ar,ar^2. now

[itex]\frac{2}{c-a}=\frac{1}{a-b}+\frac{1}{b-c} \\

r^2+4r+1=0[/itex]

Since both roots are +ve sum and product of roots should also be +ve.

[itex]\frac{-b}{a+c}>0 \\

\frac{4b^2}{a+c}>0 \\ \\

\frac{r}{1+r^2}<0\\

\frac{4ar}{1+r^2}>0[/itex]