What is x if x^2+(1/x^2)+x+(1/x)=4 ?

x^2 + ( 1/x^2 ) + x + 1/x =
4

First we will re-write into two
parts.

==> ( x^2 + 1/x^2 ) + ( x+ 1/x) =
4

Let x + 1/x =
y..............(1)

==> (x+ 1/x)^2 =
y^2

=> x^2 + 2 + 1/x^2 =
y^2

==> x^2 + 1/x^2 = y^2 -
2............(2)

Now we will substitute ( 1) and
(2).

==> (y^2 - 2 ) + ( y) =
4

==> y^2 + y - 2 =
4

==> y^2 + y - 6  =
0

==> ( y + 3) ( y-2) =
0

==> y1=
-3 

 ==> x + 1/x  =
-3

==> x^2 + 1 =
-3x

==> x^2 + 3x + 1 =
0

==> x1 = ( -3 + sqrt(5)
/2

==> x2= (
-3-sqrt5)/2

==> y2=
2

==> x+ 1/x =
2

==> x^2 + 1 =
2x

==> x^2  -2x + 1
=0

==> ( x-1)^2 =
0

==> x= 1

Then x
values are:

x = { 1, (-3+sqrt5)/2 ,
(-3-sqrt5)/2}