Question

Find the term of
(x + 1/x)6 that does not contain x​

Answer 1

Answer:

Tr+1=6Cr.(x)^(6-r).(-1/x)^r

or. =6Cr.(-1)^r.(x)^(6-r-r).

or. =6Cr.(-1)^r. (x)^(6–2r)……………(1)

For constant term power of x should zero.

6–2r=0. =>. r=3

On putting r=3 in eqn.(1)

T(3+1) =6C3.(-1)^3.(x)^(6–6)

T4. = - 6.5.4.(3!)/(3!).(3.2.1) .(x)^0

T4= -20.(1)

T4 = -20. Answer.

Answer 2

Answer:

The term not containing $x$ is $20$.

Step-by-step explanation:

We are given $(x+\frac{1}{x} )^{6}$.

We need to determine the term that does not contain $x$.

This based on binomial theorem.

The binomial theorem states the principle for expanding the algebraic expression and expresses it as a sum of the terms involving individual exponents of variables.

Here,

Tr+1=6Cr.(x)^(6-r).(-1/x)^r

=6Cr.(-1)^r.(x)^(6-r-r)

=6Cr.(-1)^r. (x)^(6–2r)………(1)

Power of x should zero for constant term.

6–2r=0.

r=3

Using r=3 in (1)

T(3+1) =6C3.(-1)^3.(x)^(6–6)

T4. = - 6.5.4.(3!)/(3!).(3.2.1) .(x)^0

T4= -20.(1)

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