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

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T_{2}

T_{1}

T_{3}

T_{4}

answer is C.

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Detailed Solution

The given expression is,

{(x + \frac{1}{x})}^{4}

Here, the independent term

T_{r + 1} = 4_{{Cr}_{r}} x^{4 r} {(\frac{1}{x})}^{r}

T_{r + 1} = 4_{{Cr}_{r}} \frac{x^{4 - r}}{x^{r}}

T_{r + 1} = 4_{{Cr}_{r}} x^{4 - 2 r}

Here, the exponent of x should be equal to zero to make the term independent of x. Thus,

4 - 2 r = 0

r = 2

Put this left hand side we get,

\Rightarrow T_{2 + 1} = T_{3}

So,

T_{3}

is the term, which is independent term from x of the expansion.
Correct option is 3.

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