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))=0,(√(3)x √(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

$3 x^{2} - \sqrt{6} x - \sqrt{6} x + 2 = 0$
$\sqrt{3} x (\sqrt{3} x - \sqrt{2}) - \sqrt{2} (\sqrt{3} x - \sqrt{2}) = 0$
$(\sqrt{3} x - \sqrt{2}) (\sqrt{3} x - \sqrt{2}) = 0$
$(\sqrt{3} x - \sqrt{2}) = 0, (\sqrt{3} x - \sqrt{2}) = 0$
$x = \frac{\sqrt{2}}{\sqrt{3}}$

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