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If α and β be the coefficients of x4 and x2 respectively in the expansion of (x + √(x2 − 1))6 + (x − √(x2 − 1)6, then:
1. α + β = −30
2. α − β = −132
3. α − β = 60
4. α + β = 60

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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)+ (x−y)= 2[C0 x+ C2 xn-1 y+ C4 xn-4 y+ …]

⇒ (x + y)– (x−y)= 2[C1 xn-1 y + C3 xn-3 y+ C5 xn-5 y+ …]

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