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If (x+1/x+1)^(6)=a(0)(a(1)x+(b1)/x) +(a(...

If `(x+1/x+1)^(6)=a_(0)(a_(1)x+(b1)/x)`
`+(a_(2)x^(2)+b_(2)/x^(2))+...+(a_(6)x^(6)+b_(6)/x^(6)),`
the value of `a_(0)` is

A

121

B

131

C

141

D

151

Text Solution

Verified by Experts

The correct Answer is:
c
`because (x+1/x+1)^(6) = sum_(r=0)^(6) ""^(6)C_(r) (x+1/x)^(r)` for constant term r
must be even integer.
`therefore a_(0) = ""^(6)C_(0) + ""^(6) C_(2) xx^(2) C_(1) +""^(6)C_(4)xx^(4) C_(2) +""^(6) C_(6) xx""^(6)C_(3)`
`= 1 + 30 + 90 + 20 =141`
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