Let `p ,q` be integers and let `alpha,beta` be the roots of the equation, `x^2-x-1=0,` where `alpha!=beta` . For `n=0,1,2, ,l e ta_n=palpha^n+qbeta^ndot` FACT : If `aa n db` are rational number and `a+bsqrt(5)=0,t h e na=0=bdot` If `a_4=28 ,t h e np+2q=` 7 (b) 21 (c) 14 (d) 12

Let A,B be integers and let alpha,beta be the roots of the equation,x^(2)-x-1=0, where alpha!=beta For n=0,1,2,..., Let a_(n)=A alpha^(-n)+B beta^(-n)

Let p ,q be integers and let alpha,beta be the roots of the equation, x^2-x-1=0, where alpha!=beta . For n=0,1,2, .....,l e ta_n=palpha^n+qbeta^ndot FACT : If aa n db are rational number and a+bsqrt(5)=0,t h e na=0=bdot a_(12)= (a)a_(11)+a_(10) (b) a_(11)-a_(10) (c)a_(11)+2a_(10) (d) 2a_(11)+a_(10)

Let p,q be integers and let alpha,beta be the roots of the equation x^(2)-2x+3=0 where alpha!=beta For n=0,1,2,......, Let alpha_(n)=p alpha^(n)+q beta^(n) value alpha_(9)=

Let alpha and beta be the roots of the equation 5x^2+6x-2=0 . If S_n=alpha^n+beta^n, n=1,2,3.... then

If alpha and beta are the roots of the equation x^(2)-ax+b=0 and A_(n)=alpha^(n)+beta^(n)

Let alpha and beta be the roots of the equation 5x^2 + 6x-2 =0 if S_(n ) = alpha ^(n) + beta^(n) , n= 1,2,3 ..,, then :