Question

Root 3 x2- 2root2x -2 root 3
= 0

Answer 1

$\sf{\underline{\underline{Given :}}}$


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


$\sf{Using \ Middle \ Term \ Factorisation, \ we \ get}$


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


$\sf{{\sqrt{3}} x (x - {\sqrt{6}} ) + {\sqrt{2}} (x - {\sqrt{6}} ) = 0}$


$\sf{( {\sqrt{3}} x + {\sqrt{2}} )(x - {\sqrt{6}} ) = 0}$


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


${\boxed{\sf{x = {\dfrac{-{\sqrt{2}}}{{\sqrt{3}}}} \ \ and \ \ x = {\sqrt{6}}}}}$

Answer 2

$\sqrt{3} {x}^{2} - 2 \sqrt{2} x - 2 \sqrt{3} \\ x = \frac{ - b + - \sqrt{ {b}^{2} - 4ac} }{2a} \\ x = \frac{2 \sqrt{2} + - \sqrt{8 + 24} }{2 \sqrt{3} } \\ x = \frac{2 \sqrt{2} + - \sqrt{32} }{2 \sqrt{3} } \\ x = \frac{2 \sqrt{2} + - 4 \sqrt{2} }{2 \sqrt{3} } \\ x = \frac{ \sqrt{2} + - 2 \sqrt{2} }{ \sqrt{3} } \\ x = \frac{3 \sqrt{2} }{ \sqrt{3} } \: or \: x = - \frac{ \sqrt{2} }{ \sqrt{3} } \\ x = \sqrt{6} \: or \: x = - \frac{ \sqrt{6} }{3}$
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