b)
$PT\Leftrightarrow \sqrt{2(x^{2}-2x+2).(x^{2}+2x+2)}=4(x^{2}-2x+2)-(x^{2}+2x+2)$
$\Leftrightarrow 4.\frac{x^{2}-2x+2}{x^{2}+2x+2}-\sqrt{2}.\sqrt{\frac{x^{2}-2x+2}{x^{2}+2x+2}}-1=0$
$\Leftrightarrow \sqrt{\frac{x^{2}-2x+2}{x^{2}+2x+2}}=\frac{\sqrt{2}}{2}\Leftrightarrow x=3\pm \sqrt{7}$.