Question

Factorise: $x^2-5x+\frac{25}{4}$

Answer 1

Answer:

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

Step-by-step explanation:

$x^2-5x+\dfrac{25}{4}$

Factorise by completing the square method

Add and subtract (b/2)²:

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

Complete the square:

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

Evaluate the terms outside the bracket:

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

Answer 2

Solution :

Given quadratic expression :

x² - 5x + 25/4

Splitting the middle term , we get

= x² - 5x/2 - 5x/2 + 25/4

= x( x - 5/2 ) - 5/2 ( x - 5/2 )

= ( x - 5/2 )( x - 5/2 )

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Or

x² - 5x + 25/4

= x² - 2*x*5/2 + ( 5/2 )²

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We know the algebraic identity:

a² - 2ab + b² = ( a - b )²

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= ( x - 5/2 )²

= ( x - 5/2 )( x - 5/2 )

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