Question

Let α and β be the roots of x² – 6x – 2 = 0. If a_n = αⁿ – βⁿ for n ≥ 1, then the value of (a₁₀ – 2a₈)(2a₉) is

Answer 1

The correct option is (3) 3.

The given quadratic equation is

x² - 6x - 2 = 0  .....(i)

And α and β be the roots of this equation

Substituting x = α in (i)

α² - 6α - 2 = 0

α² - 2 = 6α    ........(ii)

And substituting x = β in (i)

β² - 6β - 2 = 0

β² - 2 = 6 ..........(iii)

Since given that a_n = αⁿ - βⁿ

Therefore,