Determine the solution set for the following: (3x+1/x)^2 - (12x+4/x)+4=0

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`(3x+1/x)^2-(12x+4/x)+4 = 0`

This is easy if we make a substitution as, `t = 3x+1/x`

Then the equation changes to,

`t^2-4t+4 = 0`

First let's solve for t,

`(t-2)(t-2) = 0`

t = 2.

The solution for t is 2.

Therefore, `3x+1/x = 2.`

This gives,

`3x^2+1 = 2x`

`3x^2-2x+1 = 0`

Now let's sovle for x,

This gives complex solutions as,

`x = (1+-sqrt(2)i)/3`

 

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