Question

How to solve this equation 4x²-4x+1=0?

Answer 1

4`x^2` -4`x`+1=0
4`x^2`-2`x`-2`x`+1=0
2`x`(2`x`-1)-1(2`x`-1)=0
(2`x`-1)(2`x`-1)=0
`(2`x`-1)^2`=0
2`x`=1
threfore ,
`x` = `1/2`

Here I have used middle-term technique to factorize the equation

Answer 2

`x=1/2" multiplicity 2"`

Explanation:

`"Using the a-c method to factor the quadratic"`

`"the factors of + 4 which sum to - 4 are - 2 and - 2"`

`rArr4x^2-2x-2x+1=0larrcolor(blue)"split the middle term"`

`rArrcolor(red)(2x)(2x-1)color(red)(-1)(2x-1)=0larrcolor(blue)"factor by grouping"`

`"Take out a common factor "(2x-1)`

`rArr(2x-1)(color(red)(2x-1))=0`

`rArr(2x-1)^2=0`

`rArr2x-1=0rArrx=1/2" twice"`