Correct Answer - Option 2 :
α − β = −132
Calculation:
(x + √(x2 − 1))6 + (x − √(x2 − 1)6
⇒ 2[6C0 x6 + 6C2x4(x2 – 1) + 6C4x2(x2 – 1)2 + 6C6(x2 – 1)3]
⇒ 2[32x6 – 48x4 + 18x2 – 1]
⇒ α = -96 and β = 36
⇒ α – β = -132
⇒ (x + y)n + (x−y)n = 2[C0 xn + C2 xn-1 y2 + C4 xn-4 y4 + …]
⇒ (x + y)n – (x−y)n = 2[C1 xn-1 y + C3 xn-3 y3 + C5 xn-5 y5 + …]