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If $α, β$ are the roots of $x^{2} - ax + b = 0$ and if $α^{n} + β^{n} = V_{n},$ then

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a

Vn+1=aVn+bVn-1

b

Vn+1=aVn+aVn-1

c

Vn+1=aVn-bVn-1

d

Vn+1=aVn-1-bVn

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detailed solution

Correct option is C

Multiplying x2-ax+b=0 by xn-1xn+1-axn+bxn-1=0 ...(i)α,β are roots of x2-ax+b=0, therefore they will satisfy (i) also αn+1-aαn+bαn-1=0 ...(ii)and βn+1-αβn+bβn-1=0 ...(iii)adding (ii) and (iii)(αn+1+βn+1)-a(αn+βn)+b(αn-1+βn-1)=0or Vn+1=aVn-bVn-1(Given αn+βn=Vn)

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