Sure! Let's find [tex]\( x + \frac{1}{x} \)[/tex] given that [tex]\( x = 2 + \sqrt{3} \)[/tex].
1. Identify the value of [tex]\( x \)[/tex]:
[tex]\[
x = 2 + \sqrt{3}
\][/tex]
2. Compute [tex]\( \frac{1}{x} \)[/tex]:
To find [tex]\( \frac{1}{x} \)[/tex], we recognize that we need to rationalize the denominator. However, we can use the given value directly. Thus:
[tex]\[
\frac{1}{x} \approx 0.2679491924311227
\][/tex]
3. Add [tex]\( x \)[/tex] and [tex]\( \frac{1}{x} \)[/tex]:
Now, simply add [tex]\( x \)[/tex] and [tex]\( \frac{1}{x} \)[/tex]:
[tex]\[
x + \frac{1}{x} = (2 + \sqrt{3}) + 0.2679491924311227
\][/tex]
4. Final Calculation:
The result for this operation is given as:
[tex]\[
x + \frac{1}{x} \approx 4.0
\][/tex]
Therefore, the value of [tex]\( x + \frac{1}{x} \)[/tex] when [tex]\( x = 2 + \sqrt{3} \)[/tex] is [tex]\( 4 \)[/tex].
