Sure! Let's solve the problem step-by-step. The given expression is \( a = 6 - \sqrt{35} \) and we need to find the value of \( a + \frac{1}{a} \).
1. Value of \( a \):
The value of \( a \) is directly given:
[tex]\[
a = 6 - \sqrt{35}
\][/tex]
2. Calculate \( \frac{1}{a} \):
To find \( \frac{1}{a} \), we need to take the reciprocal of \( a \):
[tex]\[
\frac{1}{a} = \frac{1}{6 - \sqrt{35}}
\][/tex]
Preparing it further, without losing the general meaning, it simplifies to:
[tex]\[
\frac{1}{a} = 11.916079783099628
\][/tex]
3. Add \( a \) and \( \frac{1}{a} \):
Now, we add the value of \( a \) and the value of \( \frac{1}{a} \):
[tex]\[
a + \frac{1}{a} = 0.08392021690038387 + 11.916079783099628
\][/tex]
4. Final Result:
Adding these two values together, we get:
[tex]\[
a + \frac{1}{a} = 12.00000000000001
\][/tex]
Therefore, the value of \( a + \frac{1}{a} \) is
[tex]\[
\boxed{12.00000000000001}
\][/tex]
