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 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 . Then a_(12) is

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,..., let a_(n)=p alpha^(n)+q beta^(n). FACT : If a and b are rational number and a+b sqrt(5)=0, then a=0=b. If a_(4)=28, then p+2q=7 (b) 21( c) 14 (d) 12

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=palpha^n+qbeta^n value alpha_9=

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

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