Question

Solve $x^2-4x+1=0$ by Completing Square Method.

Answer 1

Given:

$x^2-4x+1=0$

Adding and subtracting $4$in the given equation,

$$\begin{gathered} \Rightarrow x^2+4-4x-4+1=0 \\ \Rightarrow {\left(x-2\right)}^2-4+1=0 \\ \Rightarrow {\left(x-2\right)}^2=3 \end{gathered}$$

$\Rightarrow \left(x-2\right)=+\sqrt{3}or,-\sqrt{3}$

$\Rightarrow x=2+\sqrt{3}orx=2-\sqrt{3}$

Hence, the value of $x$ is $2+\sqrt{3}$ or $2-\sqrt{3}$