Let p,q be integers and let α,β be the roots of the equation, x2−x – InterviewSolution

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1.	Let p,q be integers and let α,β be the roots of the equation, x2−x−1=0, where α≠β. For n=0,1,2,...., let an=pαn+qβn.FACT: If a and b are rational numbers and a+b√5=0. then a=0=b. a12=
Answer» Let $p, q$ be integers and let $α, β$ be the roots of the equation, $x^{2} - x - 1 = 0,$ where $α \neq β .$ For $n = 0, 1, 2, . . . .,$ let $a_{n} = p α^{n} + q β^{n} .$ FACT: If $a$ and $b$ are rational numbers and $a + b \sqrt{5} = 0.$ then $a = 0 = b .$ $a_{12} =$

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