Let P n = α n + β n , n ∈ N . If P 10 = 123 , P 9 = 76 , P 8 = 47 and P 1 = 1 , then the quadratic equation having roots α 1 and β 1 is :

Question

Let P n ​ = α n + β n , n ∈ N . If P 10 ​ = 123 , P 9 ​ = 76 , P 8 ​ = 47 and P 1 ​ = 1 , then the quadratic equation having roots α 1 ​ and β 1 ​ is :

TestHub · Accepted Answer

​ α 10 + β 10 = 123 α + β = 1 α 9 + β 9 = 76 α 8 + β 8 = 47 P 10 ​ = P 9 ​ + P 8 ​ x 2 = x + 1 ⇒ x 2 − x − 1 = 0 α + β = 1 , α β = − 1 α 1 ​ + β 1 ​ = α β α + β ​ = − 1 1 ​ = − 1 , α β 1 ​ = − 1 ​

Mathematics - Quadratic Equation Question with Solution | TestHub

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