JEE-Mains 2015 (3/30)

Algebra Level 3

Let α\alpha and β\beta be the roots of equation x26x2=0x^2-6x-2=0.

If an=αnβna_n=\alpha^n-\beta^n for n1,n \geq 1, then the value of a102a82a9\dfrac{a_{10}-2a_8}{2a_9} is equal to __________.\text{\_\_\_\_\_\_\_\_\_\_}.

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