If-the-sum-of-the-coefficients-in-the-expansion-of-1-3x-10x-2-n-is-a-and-if-the-sum-of-the-coefficients-in-the-expansion-of-1-x-2-n-is-b-then-

Question Number 63941 by gunawan last updated on 11/Jul/19

If the sum of the coefficients in the expansion

of {(1 - 3 x + 10 x^{2})}^{n} is a and if the sum of the

coefficients in the expansion of {(1 + x^{2})}^{n} is

b, then

Answered by mr W last updated on 11/Jul/19

{(1 - 3 x + 10 x^{2})}^{n} = Σ A_{r} x^{r}

l e t x = 1 :

{(1 - 3 + 10)}^{n} = Σ A_{r} = a

\Rightarrow a = 8^{n} = 2^{3 n} = {(2^{n})}^{3}

{(1 + x^{2})}^{n} = Σ B_{r} x^{r}

l e t x = 1 :

{(1 + 1)}^{n} = Σ B_{r} = b

\Rightarrow b = 2^{n}

\Rightarrow a = b^{3}

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