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

A)
`(x - 4)^2 = 3`

Explanation:

The given equation is
`x^(2) -8x +13 = 0`

We have to convert this quadratic equation in the form of
`(x -a)^(2) = b`.

Here we have to use the completing square method.

Identify the value of b from the given quadratic equation.

b = -8 now divide it by 2 and square it.

`((b)/(2))^(2)`

=
`((-8)/(2) )^2`

=
`(-4)^(2)`

= 16

Now add 16 on both side of the equation

`x^(2) - 8x + 16 + 13 = 16`

`(x^(2) -8x +16) +13 = 16`

Now subtract 13 on both sides, we get

`(x^(2) - 8x +16) + 13 -13 = 16 -13`

`x^(2) -8x + 16 = 3`

Here
`(x -4)^(2) = x^2 -8x +16`

So, we get

`(x - 4)^2 = 3`

Therefore, answer is A)
`(x - 4)^2 = 3`

Answer 2

The question is asking to write x^2-8x+13 in the form of (x-1)2 = b where as a and b are integers, base on the said formula, I would say that the correct answer would be (x - 4)2 = 3, I hope you are satisfied with my answer and feel free to ask for more if you have questions and further clarifications