Let and be the roots of x^2-6x-2=0, with . If a_n= ^n- ^n for n 1, then the value of a_10-2a_82a_9 is (IIT-JEE, 2011)

Question

Let and be the roots of x^2-6x-2=0, with > . If a_n= ^n- ^n for n 1, then the value of a_10-2a_82a_9 is (IIT-JEE, 2011)

Accepted Answer

Correct answer: C. (c) a_n= ^n- ^n Also ^2-6 -2=0 Multiply with ^8 on both sides ⇒ ^10-6 ^9-2 ^8=0 … (i ) similarly ^10-6 ^9-2 ^8=0 … . ( ii ) Subtracting (ii) from (i) we have ^10- ^10-6( ^9- ^9)=2( ^8- ^8) ⇒a_10-6a_9=2a_8 ⇒ a_10-2a_82a_9=3 .

$Let α and β be the roots of x^{2} - 6 x - 2 = 0, with α > β . If a_{n} = α^{n} - β^{n} for n \geq 1, then the value of \frac{a _{10} - 2 a _{8}}{2 a _{9}} is (IIT-JEE, 2011)$

Solution

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