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# α & β are the roots of eqn. x2-p(1+x)-c =0find value of  ( α2+2α+1/α2+2α+c ) +  (β2+2β+1/β2+2β+c )1) 12) 23) 34) None of these Badiuddin askIITians.ismu Expert
148 Points
11 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)/2+2β+c )

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

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

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

put the value

2 + -1

=1

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