a) If 𝑥 = 2 + √3, find the value of 𝑥 + 1𝑥

Sure, here are the steps to solve the problem:

Step 1: Given 𝑥 = 2 + √3

Step 2: To find the value of 𝑥 + 1/𝑥, we first need to find the value of 1/𝑥.

Step 3: To find 1/𝑥, we can use the formula for the reciprocal of a binomial a + b, which is 1/(a + b) = 1/a - b/a^2.

Step 4: Substituting a = 2 and b = √3 into the formula, we get 1/𝑥 = 1/2 - √3/4.

Step 5: Now, we can find the value of 𝑥 + 1/𝑥 by adding 𝑥 and 1/𝑥 together.

Step 6: 𝑥 + 1/𝑥 = (2 + √3) + (1/2 - √3/4) = 2.5 + 0.25√3.

So, the value of 𝑥 + 1/𝑥 is 2.5 + 0.25√3.