Solve: $3 x^{2} - 2 x + \frac{1}{3} = 0$

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Solution

$3 x^{2} - 2 x + \frac{1}{3} = 0$

$\Rightarrow 9 x^{2} - 6 x + 1 = 0$

$\Rightarrow (3 x)^{2} - 2 (3 x) (1) + (1)^{2} = 0$ [Using $a^{2} - 2 a b + b^{2} = (a - b)^{2}$ ]

$\Rightarrow (3 x - 1)^{2} = 0$

$\Rightarrow (3 x - 1) = 0$ or $(3 x - 1) = 0$

$x = \frac{1}{3}$ or $x = \frac{1}{3}$

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