If `a, b` and `c` also represent the sides of a triangle and `a,b,c` are in g.p then the complete set of `alpha^2 = (r^2 +r +1)/(r^2-r+1)`is

Options

A. `(1/3,3)`
B. `(2,3)`
C. `[1/3,2]`
D. `(sqrt(5+3)/2,3)`

Answer

D

Explanation

Let b=ar,c=`ar^(2)andrgt0`
As the sum of two sides is more than the third side, we have
`rin((sqrt5-1)/2,(sqrt5+1)/2)` - {1}
`rArrr+1/r-1in(1,sqrt5-1)`
As `alpha^(2)=(r^(2)+r+1)/(r^(2)-r+1)=1+2/(r+1/r-1)`
`thereforealpha^(2)in((sqrt5+3)/2,3)`