If the middle term in the expansion of (x + b/x)^6 is 160, find b.

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If the middle term in the expansion of (x + b/x)6 is 160, find b.

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Here, a = x, b = b/x, n = 6.

Now, n is even.

$\therefore$ $\frac{n+2}2=\frac{6+2}2=4$

$\therefore$ Middle term is t4, for which r = 3

$\therefore$ t4 = 160

We have

$\therefore$ 160 = b3

$\therefore$ b = 2