3x^2 2√(6)x+2=0 3x^2 √(6)x √(6)x+2=0 √(3)x(√(3)x √(2)) √(2)(√(3)x √(2))=0 (√(3)x √(2))(√(3)x √(2))=0 (√(3)x √(2))^2=0 x=√(2)√(3) ...

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Roots of Quadratic Equation

Solve: 3x2-2...

Question

Solve:
$3 x^{2} - 2 \sqrt{6} x + 2 = 0$

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Solution

$3 x^{2} - 2 \sqrt{6} x + 2 = 0$

$3 x^{2} - \sqrt{6} x - \sqrt{6} x + 2 = 0$

$\sqrt{3} x (\sqrt{3} x - \sqrt{2}) - \sqrt{2} (\sqrt{3} x - \sqrt{2}) = 0$

$(\sqrt{3} x - \sqrt{2}) (\sqrt{3} x - \sqrt{2}) = 0$

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

$x = \frac{\sqrt{2}}{\sqrt{3}}$

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