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KVPY2010MathematicsSequences and Series

Suppose the sides of a triangle form a geometric progression with common ratio r. Then r lies in the interval-

Options

  1. A(0, -1+ 5 2 ]
  2. B( 1+ 5 2 , 2+ 5 2 ]
  3. C( -1+ 5 2 , 1+ 5 2 ]
  4. D( 2+ 5 2 , )

Correct answer

C. ( -1+ 5 2 , 1+ 5 2 ]

Step-by-step solution

array l a+a r>a r² r²-r-1 a r²+r-1>0 r> -1+ 5 2 , r ar ; r ²- r +1>0 always true ving (1) & (2) r ( 5 -1 2 , 5 +1 2 )

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