If α and β be the roots of the equation x 2 - 2 x + 2 = 0 , then the least value of n for which α β n = 1 is

Question

If α and β be the roots of the equation x 2 - 2 x + 2 = 0 , then the least value of n for which α β n = 1 is, 5, 4, 2, 3

MARKS App · Accepted Answer

x 2 - 2 x + 2 = 0 ⇒ ( x - 1 ) 2 + 1 = 0 ⇒ x = 1 ± i , i = - 1 Now let the roots α = i + i & β = 1 - i α β n = 1 + i 1 - i n = i 1 - i 1 - i n ⇒ α β n = ( i ) n Using given information, ⇒ ( i ) n = 1 ⇒ The minimum value of n ∈ N = 4 because i 4 = 1 .

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