Question

If $x^2-4x+1=0$ and $x\ne 0,$ find the roots of the equation.

Answer 1

Consider the given equation ,$x^2-4x+1$ and x=$x\ne 0$

Now ,compare equation $x^2-4x+1=0$ with $a{x}^2+bx+c=0$ ,

We get $a=1,b=-4,c=1$

Now, using the quadratic formula

$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

$=\frac{4\pm \sqrt{16-4\times 1\times 1}}{2\times 1}=\frac{4\pm \sqrt{12}}{2}$

$=\frac{2\pm 2\sqrt{3}}{1}=2\pm 2\sqrt{3}$

hence,$x=2+2\sqrt{3},2-2\sqrt{3}$

This is the answer .