1.

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) 12A. `a_(11)+2alpha_(10)`B. `2a_(11)+2a_(10)`C. `a_(11)-a_(10)`D. `a_(11)+a_(10)`

Answer» Correct Answer - D
`alpha^(2)=alpha+1`
`beta^(2)=beta+1`
`a_(n)=palpha^(n)=qbeta^(n)`
`=p(alpha^(n-1)+alpha^(n-2))+q(beta^(n-1)+beta^(n-2))`
`=a_(n-1)+a_(n-2)`
`thereforea_(12)=a_(11)+a_(10)`


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