InterviewSolution
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InterviewSolution
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Consider three distinct real numbers a,b,c in a G.P with a^2+b^2+c^2=t^2 and a+b+c =alpha t .The sum of the common ratio and its reciprocal is denoted by S. Complete set of alpha^2 is |
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Answer» `(1/3,3)` `(a^(2)+a^(2)R^(2)+a^(2)r^(4))/((a+ar+ar^(2))^(2))=t^(2)/(alpha^(2)t^(2))=1/alpha^(2)` `alpha^(2)=(r^(2)+r+1)/(r^(2)-r+1)` LET `alpha^(2)=y`, `thereforey=(r^(2)+r+1)/(r^(2)-r+1)` `(y-1)r^(2)-r(y+1)+(y-1)=0` For REAL r, `(y+1)^(2)-4(y-1)^(2)ge0` `rArr1/3leyle3` But `ne1//3,1,3``(becauserne1,-1,0)` `therefore1/3ltylt3andyne1` `alpha^(2)in(1/3,3)-{1}` |
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