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

Options

A. 1
B. 2
C. `-1`
D. 0

Answer

To solve the equation \(\frac{a}{b} + \frac{b}{a} = 2\), we will follow these steps:

### Step 1: Rewrite the equation
Start with the given equation:
\[ \frac{a}{b} + \frac{b}{a} = 2 \]

### Step 2: Find a common denominator
The common denominator for the left-hand side is \(ab\). Rewrite the equation:
\[ \frac{a^2 + b^2}{ab} = 2 \]

### Step 3: Cross-multiply
Cross-multiply to eliminate the fraction:
\[ a^2 + b^2 = 2ab \]

### Step 4: Rearrange the equation
Rearranging gives:
\[ a^2 + b^2 - 2ab = 0 \]

### Step 5: Factor the equation
Recognize that the left-hand side can be factored as a perfect square:
\[ (a - b)^2 = 0 \]

### Step 6: Solve for \(a - b\)
Taking the square root of both sides, we find:
\[ a - b = 0 \]

### Conclusion
Thus, the value of \(a - b\) is:
\[ \boxed{0} \]

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