Question

# Show that the expansion of (x2+1x)12 does not contian any term involving x−1.

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Solution

## Any term in the expansion of (x2+1x)12 is TN=Tr+1=nCrxn−ryr =12Cr(x2)12−r(1x)12 =12Crx24−2rx−12 =x12−2r=x−1 12-2r=-1 2r=13 r=132 r can not be a fraction, therefore there is no term in the expansion of (x2+1x)12having the term x−1.

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