Question

Rút gọn

\(\sqrt{1-4a+4a^2}-2a\)

Answer 1

`sqrt{1-4a+4a^2}-2a`

`=sqrt{(1-2a)^2}-2a`

`=|1-2a|-2a`

`TH1: a <= 1/2`

`=>1-2a >= 0`

`=> |1-2a|=1-2a`

Ta có:

`|1-2a|-2a=1-2a-2a=1-4a`

`TH2:a > 1/2`

`=> 1-2a<0`

`=>|1-2a|=-(1-2a)=2a-1`

Ta có:

`|1-2a|-2a=2a-1-2a=-1`

Answer 2

\(\sqrt{1-4a+4a^2}-2a\)

\(=\sqrt{\left(1-2a\right)^2}-2a\)

\(=\left|1-2a\right|-2a\)

`@` Với \(a\le\dfrac{1}{2}\) \(\Rightarrow\left|1-2a\right|-2a=1-2a-2a=1-4a\)

`@`Với \(a>\dfrac{1}{2}\) \(\Rightarrow\left|1-2a\right|-2a=2a-1-2a=-1\)

Answer 3

\(=\sqrt{\left(1-2a\right)^2}-2a=\left|1-2a\right|-2a\\ TH1:a\le\dfrac{1}{2}\\ \Rightarrow\left|1-2a\right|-2a=1-2a-2a=1-4a\\ TH2:a>\dfrac{1}{2}\\ \Rightarrow\left|1-2a\right|-2a=2a-1-2a=-1\)