If w is a non-real cube root of unity, x is a real number and `n in N` such that first three terms in the binomial expansion of `(w + x)^n` are `1,12bar w and 69 w` respectively, then

Options

A. ` n = 36, x = 1`
B. n = 12, x=2
C. ` n = 24, x = (1)/(2)`
D. ` n = 18, x = (1)/(3)`

Explanation

To solve the problem, we will follow the steps outlined in the video transcript and derive the values of \( n \) and \( x \) systematically.

### Step 1: Understanding the Binomial Expansion
The binomial expansion of \( (w + x)^n \) can be expressed as:
\[ (w + x)^n = \sum_{k=0}^{n} \binom{n}{k} w^{n-k} x^k \]
We are interested in the first three terms of this expansion:
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