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 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 alpha, beta are the roots of the equation x^(2)+x+1=0 , then alpha^3-beta^3

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 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 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 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

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