how to solve this quadratic equation

Question

$n^2-4n+2=0$ I have tried many things for this but I cant resolve the roots

here $n$ should be a positive whole number as it stands for time.

Answer 1

Using the discriminant $$\Delta=4^2-4\times 2=8$$ so the roots are $$n_1=\frac12(4+\sqrt8)\qquad n_2=\frac12(4-\sqrt8)$$ and these two roots are irrational.

Answer 2

$$\Delta=(-4)^2-4 \cdot 2=16-8=8$$

$$n_{1,2}=\frac{4 \pm \sqrt{8}}{2}=\frac{4 \pm 2\sqrt{2}}{2}=2 \pm \sqrt{2}$$

So,the roots are $2 + \sqrt{2}$ and $2 - \sqrt{2}$ (both of them are positive).

Answer 3

Hint $\ n^2- 4n+2 = 0 \,\Rightarrow\, (n-2)^2 = 2\,\Rightarrow\,n\,$ irrational