Answer
{$\frac{1\pm2\sqrt 3}{3}$}
Work Step by Step
$(3x-1)^{2}=12$
Using generalized square root property, $3x-1=\pm\sqrt (12)$
$3x-1=\pm\sqrt (4\times3)$
$3x-1=\pm\sqrt 4\sqrt 3$
$3x-1=\pm2\sqrt 3$
Adding 1 to both sides, $3x-1+1=1\pm2\sqrt 3$
$3x=1\pm2\sqrt 3$
Dividing both sides by 3, $\frac{3x}{3}=\frac{1\pm2\sqrt 3}{3}$
$x=\frac{1\pm2\sqrt 3}{3}$
Check:
$(3(\frac{1+2\sqrt 3}{3})-1)^{2}=12$
$(1+2\sqrt 3-1)^{2}=12$
$(2\sqrt 3)^{2}=12$
$4(\sqrt 3)^{2}=12$
$4(3)=12$
$12=12$
$(3(\frac{1-2\sqrt 3}{3})-1)^{2}=12$
$(1-2\sqrt 3-1)^{2}=12$
$(-2\sqrt 3)^{2}=12$
$4(\sqrt 3)^{2}=12$
$4(3)=12$
$12=12$
Therefore, the solution set is {$\frac{1\pm2\sqrt 3}{3}$}
