Um... Thanks for your help, people, but... Well, first of all, I have my maths in Russian, and those English math terms are a bit confusing. And secondly,

I have asked my maths teacher today, and she solved that problem in less than a minute.

I'm sure the simplicity of it will surprise you all.

Here's how you actually supposed to do that:

x<SUP>2</SUP> + x + x<SUP>-1</SUP> + x<SUP>-2</SUP> = 4

(x<SUP>2</SUP> + 1/x<SUP>2</SUP>) + (x + 1/x) = 4

It's common knowledge that (x + 1/x)<SUP>2 </SUP>= x<SUP>2</SUP> + 2 + 1/x<SUP>2 </SUP>
<SUP></SUP>
Therefore x<SUP>2</SUP> + 1/x<SUP>2</SUP> = (x + 1/x)<SUP>2</SUP> - 2

(x + 1/x)<SUP>2</SUP> - 2 + (x + 1/x) = 4

(x + 1/x)<SUP>2 </SUP>+ (x + 1/x) - 6 = 0

Then we say that (x + 1/x) = t and solve the t<SUP>2 </SUP>+ t - 6 = 0 quadratic equation.

Sorry for bothering all you people ^^ But this way of solving might be useful if you ever come across something like that again.

Thank you all again for bothering to help me

Selena