If \alpha and \beta be the coefficients of x4 and x2 respectively in the expansion of {\left( {x + \sqrt {{x^2} - 1} } \right)^6} + {\left( {x - \sqrt {{x^2} - 1} } \right)^6}, then

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Answer: D. \alpha - \beta = -132 (x+a)n + (x – a)n = 2(T1 + T3 + T5 +.....) {\left( {x + \sqrt {{x^2} - 1} } ight)^6} + {\left( {x - \sqrt {{x^2} - 1} } ight)^6} = 2[T1 + T3 + T5 + T7 ] = 2[6C0 x6 + 6C2 x4(x2 – 1) + 6C4 x2(x2 –1)2 + 6C6 x0(x2–1)3] = 2[x6+ 15(x6 – x4) + 15x2 (x4 + 1 –2x2) + (x6 – 3x4 +3x2 –1)] = 2[x6(2 + 15 + 15 + 1) + x4(–15 – 30 –3) + x2(15 + 3)] Coefficient of x4 = \alpha = -96 And coefficient of x2 = \beta = 36 	herefore \alpha - \beta = - 96 - 36 = -132

If $$\alpha $$ and $$\beta $$ be the coefficients of x4 and x2 respectively in the expansion of $${\left( {x + \sqrt {{x^2} - 1} } \right)^6} + {\left( {x - \sqrt {{x^2} - 1} } \right)^6}$$, then

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