Question

Express x²-5x+8 in the form (x-a)²+b where a and b are top heavy fractions.
Does anyone know how to answer this?

Answer 1

x²-5x+8 can be expressed in terms of (x-a)²+b
x²-5x-5(5/2)²+(5/2)²+8
=(x+5/2)²+7/4
here a=5/2 & b=7/4

Answer 2

Given:

$x^2 - 5x + 8$

To Find:

$\text{Put into the format : }(x - a)^2 + b$

Method To Use:

$\text{Completing the Square}$

Solution:

$x^2 - 5x + 8$

Form a set of (b/2)² into the expression:

$x^2 - 5x + (\dfrac{5}{2})^2 - (\dfrac{5}{2})^2 + 8$

Rewrite (a² - 2ab + b²)  as (a - b)² in the expression:

$\bigg(x - \dfrac{5}{2}\bigg)^2 - (\dfrac{5}{2})^2 + 8$

Combine the terms outside the (a - b)² in the expression:

$\bigg(x - \dfrac{5}{2}\bigg)^2 - \dfrac{25}{4} + 8$

$\bigg(x - \dfrac{5}{2}\bigg)^2 + \dfrac{7}{4}$

Matching the expression with (x - a)² + b:

$a = \dfrac{5}{2}$

$b = \dfrac{7}{4}$

$\boxed{\text{Answer: a =} \dfrac{5}{2} \text{ and b = } \dfrac{7}4} }$