If `(2 + sqrt3) a = (2 - sqrt3) b =1 ` then the value of `(1)/(a) + (1)/(b)` is

Options

A. 1
B. 2
C. `2sqrt3`
D. 4

Answer

To solve the problem, we start with the given equations:

\[ (2 + \sqrt{3}) a = 1 \]
\[ (2 - \sqrt{3}) b = 1 \]

From these equations, we can express \(a\) and \(b\) in terms of constants.

### Step 1: Solve for \(a\)

From the first equation, we can isolate \(a\):

\[ a = \frac{1}{2 + \sqrt{3}} \]

### Step 2: Solve for \(b\)

From the second equation, we can isolate \(b\):

\[ b = \frac{1}{2 - \sqrt{3}} \]

### Step 3: Find \(\frac{1}{a}\) and \(\frac{1}{b}\)

Now, we need to find \(\frac{1}{a}\) and \(\frac{1}{b}\):

\[ \frac{1}{a} = 2 + \sqrt{3} \]
\[ \frac{1}{b} = 2 - \sqrt{3} \]

### Step 4: Calculate \(\frac{1}{a} + \frac{1}{b}\)

Now we can add these two fractions:

\[ \frac{1}{a} + \frac{1}{b} = (2 + \sqrt{3}) + (2 - \sqrt{3}) \]

### Step 5: Simplify the expression

When we simplify the expression:

\[ \frac{1}{a} + \frac{1}{b} = 2 + \sqrt{3} + 2 - \sqrt{3} \]

The \(\sqrt{3}\) terms cancel out:

\[ \frac{1}{a} + \frac{1}{b} = 2 + 2 = 4 \]

### Final Answer

Thus, the value of \(\frac{1}{a} + \frac{1}{b}\) is:

\[ \boxed{4} \]