MHB How Do You Solve This Complex Quadratic Equation?

[paulmdrdo1]

please help me with this

$\frac{x^2+2}{x}+\frac{8x}{x^2+2}=6$

this is where I can get to when I simplify the the equation above,

$x^4-6x^3+12x^2+12x+4=0$

 

[kaliprasad]

please help me with this

$\frac{x^2+2}{x}+\frac{8x}{x^2+2}=6$

this is where I can get to when I simplify the the equation above,

$x^4-6x^3+12x^2+12x+4=0$

the above has become more complex
in case you put
$\frac{x^2+2}{x}= y$

then you get
$ y +\frac{8}{y} = 6$

you get quadratic in y then solve for y and based on it solve for x

I hope you can proceed because at no stage you get more than quadratic

 

[Amer]

please help me with this

$\frac{x^2+2}{x}+\frac{8x}{x^2+2}=6$

this is where I can get to when I simplify the the equation above,

$x^4-6x^3+12x^2+12x+4=0$

Let $ y = \frac{x^2+2}{x} $
Solve it for y
$y + \frac{8}{y} = 6 $
Then solve it for x