Question

Guys help me out please

Answer 1

Expand and then simplify using Bionomial Theorem

\[( x + \frac{ 1 }{ 2x }) ^6 + ( x - \frac{ 1 }{ 2x }) ^6 \]

Answer 2

@math&ing001
@Schrodingers_Cat

Answer 3

@math&ing001

Answer 4

Apply that on your expression.

Answer 5

Here's the binomial theorem:

\((a + b)^n = \sum _{k=0} ^n~_nC_k a^{n-k}b^{k}\)

Answer 6

Thanks both of you , but is there a quicker way to do it ? I might just face such a question which would require like 3 marks to do it during my exam .. I think using both ways would take much longer ? Isn't it ?

Answer 7

You will need:
\(_6C_0\)
\(_6C_1\)
\(_6C_2\)
\(_6C_3\)
\(_6C_4\)
\(_6C_5\)
\(_6C_6\)

Answer 8

The \(a^{n-k}b^k\) part is easy.
For the coefficients, you can use the Pascal triangle:

Answer 9

Well it might take a while but you'll have a lot of terms cancelling each other out since you have 1/2x and -1/2x.