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Given (1-2x+5x^2-10 x^3)(1+x)^n=1+a1x+a2...

Given `(1-2x+5x^2-10 x^3)(1+x)^n=1+a_1x+a_2x^2+` and that`a1 2=2a_2` then the value of `n` is.

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Verified by Experts

The correct Answer is:
6
`(1+2x+5x^(2)-10x^(3))[.^(n)C_(0) + .^(n)C_(1)x+.^(n)C_(2)x^(2)+ "…."]`
`= 1+a_(1)x+a_(2)x^(2) +"….."`
`rArr a_(1)= n-2` and `a_(2) = (n(n-1))/(2)-2n+5`
Given that `a_(1)^(2) = 2a_(2)`
`rArr (n-2)^(2) = n(n-1)-4n + 10`
or `n^(2) - 4n+4=n^(2)-5n+10`
or `n = 6`
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