Let p, q be integers and let α, β be the roots of the equation, x^2-x-1=0 where α≠β. For n=0,1,2,...

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Let p, q be integers and let α, β be the roots of the equation, x^2-x-1=0 where α≠β. For n=0,1,2, …, let a_n=p α^n+q β^n.
Fact: If a and b are rational numbers and a+b √(5)=0, then a=0=b.
If a_4=28, then p+2 q=
(1) 21
(2) 14
(3) 7
(4) 12
(JEE Advanced 2017)

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