Question

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

Answer 1

Answer:

A

Step-by-step explanation:

Answer 2

The completing the square method is important when transforming a quadratic equation to $(x - a)^2 =b$ form. The values of a and b are 4 and 3

Given:

$x^2 - 8x + 13 = 0$

Subtract 13 from both sides

$x^2 - 8x + 13 -13= 0-13$

$x^2 - 8x= -13$

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Next, we perform the following operations

Take the coefficient (k) of x

$k = -8$

Divide k by 2

$k/2 = -8/2$

$k/2 = -4$

Square both sides

$(k/2)^2 = (-4)^2$

$(k/2)^2 = 16$

Back to the equation, we add 16 to both sides

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$x^2 - 8x= -13$

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

$x^2 - 8x + 16 =3$

Expand the left-hand side

$x^2 - 4x -4x+ 16 =3$

Factorize

$x(x - 4) -4(x- 4) =3$

Factor out x -4

$(x - 4) (x- 4) =3$

Express as squares

$(x - 4)^2 =3$

Given that:

$(x - a)^2 =b$

By comparison:

$a =4;\ b =3$

The values of a and b are 4 and 3, respectively.

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