If a,b and c also represent the sides of a triangle and a,b,c are in g – InterviewSolution

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1.	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)`isA. `(1/3,3)`B. (2,3)C. `[1/3,2]`D. `(sqrt(5+3)/2,3)`
Answer» Correct Answer - D 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)`

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