Find the term independent of x in x-1x4-

Let T_r+1 be the independent term of x in the given expansion.Therefore, T_r+1=4_C_rx^4 r (1x)^r=4_C_rx^4 rx^r=4_C_rx^4 2r For the term independent of ...

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Standard XII

Mathematics

Binomial Expression

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Question

Find the term independent of x in $(x + \frac{1}{x})^{4}$ .

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Solution

Let $T_{r + 1}$ be the independent term of x in the given expansion.
Therefore,
$T_{r + 1} = {4_{C}}_{r} x^{4 - r} (\frac{1}{x})^{r} = {4_{C}}_{r} \frac{x^{4 - r}}{x^{r}} = {4_{C}}_{r} x^{4 - 2 r}$

For the term independent of x the power of x should be zero.
Therefore, $4 - 2 r = 0$
$r = 2$
$⟹ T_{2 + 1} = T_{3}$ term, is the independent term of the expansion.

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Find the term independent of x in (x+1x)4.

Let Tr+1 be the independent term of x in the given expansion.Therefore,Tr+1=4Crx4−r(1x)r=4Crx4−rxr=4Crx4−2rFor the term independent of x the power of x should be zero.Therefore, 4−2r=0r=2⟹T2+1=T3 term, is the independent term of the expansion.

Find the term independent of x in $(x + \frac{1}{x})^{4}$ .