Write x2 - 8x + 13 = 0 in the form (x - a) 2 = b, where a and b are integers. a.) (x - 4) 2 = 3 b.) (x - 3) 2 = 2 c.) (x - 2) 2 = 1 d.) (x - 1) 2 = 4

The answer is a.) (x - 4) 2 = 3.

(x - a) ² = b can be expressed as:

x² - 2ax + a² = b ⇒ x² - 2ax + a² - b = 0

Our equation is x² - 8x + 13 = 0.

The general formula is x² - 2ax + (a² - b) = 0

Thus:

8x = 2ax and a² - b = 13

Divide both sides of the first equation (8x = 2ax) by x:

8 = 2a ⇒ a = 8 : 2 = 4

Replace a in the second equation (a² - b = 13):

4² - b = 13 ⇒ b = 4² - 13 = 16 - 13 = 3

Now when we have a and b, let's just replace them in the general equation:

(x - a) ² = b

(x - 4) ² = 3