`A`, `B` be roots of x^2-6x-2=0 with A>B. If T(n)= A^n- B^n, where n is an integer. Find the numerical value of [T(2014)-2T(2012)]/T(2013).

See the question is very easy to tackle. What you need to do is derive value from the equation given. (A^2014-B^2014)-2(A^2012-B^2012)/(A^2013-B^2013) [A^2012(A^2-2)]-[B^2012(B^2-2)]/(A^2013-B^2013) Now if we put A on the equation given, A2-6A-2=0 so A2-2 = 6A So replace the values and you will get 6(A^2013-B^2013)/(A^2013-B^2013) Answer is 6. I recommend you to first copy the solution in your notebook then it will become understandable