Answer:
Option 1st is correct
\((x-4)^2 = 3\)
Step-by-step explanation:
Given equation:
\(x^2-8x+13=0\) .....[1]
To write the given equation in the form of \((x-a)^2 = b\) where, a and b are integers
Subtract 13 from both sides in [1] we have;
\(x^2-8x=-13\)
Complete the square in x-term by adding the square of half the x-coefficient \((\frac{8}{2})^2 = 16\) we have;
\(x^2-8x+4^2 = -13+16\)
Using identity rules: \((a-b)^2 = a^2-2ab+b^2\)
then;
\((x-4)^2 = 3\)
Therefore, the the given equation in the form of \((x-a)^2 = b\) is , \((x-4)^2 = 3\)
