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α & β are the roots of eqn. x 2 -p(1+x)-c =0 find value of ( α 2 +2α+1/α 2 +2α+c ) + (β 2 +2β+1/β 2 +2β+c ) 1) 1 2) 2 3) 3 4) None of these

α & β are the roots of eqn. x2-p(1+x)-c =0


find value of  ( α2+2α+1/α2+2α+c ) +  (β2+2β+1/β2+2β+c )


1) 1


2) 2


3) 3


4) None of these

Grade:12

1 Answers

Badiuddin askIITians.ismu Expert
148 Points
13 years ago

Dear Mayank

x2-p(1+x)-c =0

α & β are the roots of eqn

α2-p(1+α)-c =0   or α2 =p(1+α) +c 

β2-p(1+β)-c =0   or β2 =p(1+β) +c

and  α + β = p

     α *β =-p-c

NOw    ( α2+2α+1/α2+2α+c ) +  (β2+2β+1/β2+2β+c )

or       1 + (c-1)/(α2+2α+c )   + 1 + (c-1)/(β2+2β+c )

or       2  +(c-1)[1/(α2+2α+c )   +1/(β2+2β+c )]

or       2 + (c-1)[(α2+2α+c )   +(β2+2β+c ) ]/(α2+2α+c ) (β2+2β+c )

or       2 + (c-1) [α2+ β2+2(α+β)+2c]/[α2β2 +2αβ(α+β) +c(α2+β2)+4αβ+2c(α+β) +c2]

 put the value

         2 + -1

      =1

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Badiuddin



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