[tex]\displaystyle \\
a)~~ 3x^{2} - 2 \sqrt{3}x +1 = (x\sqrt{3})^2 + 2\times (x\sqrt{3})\times (-1)^2=(x\sqrt{3} -1)^2 \\ \\ \\
b)~~3+2 \sqrt{3} x + x^{2} =(\sqrt{3})^2 + 2\times \sqrt{3} \times x + x^2=(\sqrt{3}+x)^2 \\ \\ \\
c)~~x^{2} - \frac{2}{3} x + \frac{1}{9} = x^{2} + 2\times x \times \Big(-\frac{1}{3}\Big) + \Big(\frac{1}{3}\Big)^2 =\Big(x-\frac{1}{3}\Big)^2[/tex]
