The roots of `x + (1)/(x)` = 2 are …..

Answer

To solve the equation \( x + \frac{1}{x} = 2 \) and find its roots, we can follow these steps:

### Step 1: Rewrite the equation
We start with the given equation:
\[ x + \frac{1}{x} = 2 \]

### Step 2: Eliminate the fraction
To eliminate the fraction, we can multiply both sides of the equation by \( x \) (assuming \( x \neq 0 \)):
\[ x^2 + 1 = 2x \]

### Step 3: Rearrange the equation
Next, we rearrange the equation to form a standard quadratic equation:
\[ x^2 - 2x + 1 = 0 \]

### Step 4: Factor the quadratic equation
Now, we can factor the quadratic equation:
\[ (x - 1)(x - 1) = 0 \]
or
\[ (x - 1)^2 = 0 \]

### Step 5: Solve for \( x \)
Setting the factored form equal to zero gives us:
\[ x - 1 = 0 \]
Thus, we find:
\[ x = 1 \]

### Conclusion
The root of the equation \( x + \frac{1}{x} = 2 \) is:
\[ x = 1 \]

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