Question

*Find the middle term in the expansion of (x + 1/x)⁴.*

1️⃣ 6
2️⃣ 12
3️⃣ 6x²

4️⃣ 12x²
​

Answer 1

Answer:

sorry I can't solve your answer

Answer 2

Answer:

Middle term in the expansion of $(x + \frac{1}{x})^{4}$ is 6.

The correct answer is option (1) 6

Step-by-step explanation:

Given:

Binomial expansion $(x + \frac{1}{x})^{4}$

Find:

Middle term of the expansion

Solution:

We know that a binomial expansion $(x + y)^{n}$ contains $n+1$ terms

Given binomial expansion is $(x + \frac{1}{x})^{4}$

• Here n=4
• So, there are 4+1 = 5 terms
• The middle term of an expansion can be found by  $\frac{n}{2} + 1$
• Here, $\frac{n}{2} + 1 = \frac{4}{2} + 1 = 2+1 =3$
• Middle term = 3rd term

How to find the $r+1^{th}$ term of an expansion:

$T_{r+1}$ $= nC_{r} \ x^{n-r} \ y^{r}$

Here, to find the 3rd term,

r+1 = 3 ⇒ r = 2

n = 4

∴ $T_{3} = \ ^4C_{2} \ x^{4-2} \ y^{2}$

       $= \ ^4C_{2} \times x^{2} \times (\frac{1}{x}) ^{2}$

       $=\ 6 \times x^{2} \times \frac{1}{x^{2} }$

       $= \ 6$

∴ The middle term of the expansion $(x + \frac{1}{x})^{4}$ is 6.

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