Question

write x2 − 8x 13 = 0 in the form (x − a)2 = b, where a and b are integers. (x − 4)2 = 3 (x − 3)2 = 2 (x − 2)2 = 1 (x − 1)2 = 4

Answer 1

X^2  -8x + 13 =0

x^2 -8x = -13

x^2 - 8x +16 = - 13 + 16

(x - 4)^ = 3 That is the first option shown.

Answer 2

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 , $(x-4)^2 = 3$