Let , ( > ) be the roots of the quadratic equation x^ 2 - x - 4 = 0. If P_ n = ^ n - ^ n , n N, then (P_ 15 P_ 16 - P_ 14 P_ 16 - P_ 15 ^ 2 + P_ 14 P_ 15 )/(P_ 13 P_ 14 ) is equal to _____.

JEE Main 2022 Mathematics question

Let , be the roots of the quadratic equation . If , n N, then is equal to .

Answer: 16

Since and , $ - = (α ^{n} - α ^{n-1}) - (β ^{n} - β ^{n-1}) = α ^{n-2}(α ^{2} - α ) - β

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Question ID VK-035067