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Question:

The sum of the coefficient of all even degree terms in x in the expansion of (x+√(x³-1))⁶+(x-√(x³-1))⁶, (x>1) is equal to:

26

24

32

29

Solution:

Correct option is D. 24
(x+√(x³-1))⁶+(x-√(x³-1))⁶=2[⁶C₀x⁶+⁶C₂x⁴(x³-1)+⁶C₄x²(x³-1)²+⁶C₆(x³-1)³]=2[⁶C₀x⁶+⁶C₂x⁷-⁶C₂x⁴+⁶C₄x⁸+⁶C₄x²-2⁶C₄x⁵+(x⁹-1-3x⁶+3x³)]
→ sum of coefficient of even powers of x =2[1-15+15+15-1-3]=24