If the roots of the equation `(b-c)x^2+(c-a)x+(a-b)=0` are equal, then prove that `2b=a+c`.

Explanation

To prove that if the roots of the equation \((b-c)x^2 + (c-a)x + (a-b) = 0\) are equal, then \(2b = a + c\), we will follow these steps:

### Step 1: Identify the coefficients
The given quadratic equation is:
\[ (b-c)x^2 + (c-a)x + (a-b) = 0 \]
Here, we can identify:
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