Question

Root 3 X square + 10 x minus 8 root 3 equal to zero

Answer 1

Step-by-step explanation:

$\sqrt{3} {x}^{2} + 10x - 8 \sqrt{3} = 0 \\ \\{ \underline{\bf \pmb{ \purple{Rough: }}}}\\ \red{\sqrt{3} {x}^{2} \times - 8 \sqrt{3} = \sqrt{9} {x}^{2} \times- 8 = - 24 {x}^{2} }\\ \\ \red{ - 24 {x}^{2} = 12x \times - 2 x\: \: \& \: \: 12 x- 2x = 10x }\\ \\ \\ \Rightarrow\sqrt{3} {x}^{2} + 12x - 2x - 8 \sqrt{3} = 0 \\ \\ \\ \underline{\bf \pmb{ \purple{Rough: }}}\\ \red{\frac{12x}{ \sqrt{3} {x}^{} } = \frac{12}{ \sqrt{3} } \times \frac{ \sqrt{3} }{ \sqrt{3} } = \frac{ {}^{4} \cancel{12} \sqrt{3} }{ \cancel3} = 4 \sqrt{3} }\\ \\ \\ \Rightarrow \sqrt{3}x (x + 4 \sqrt{3} ) - 2(x + 4 \sqrt{3} ) = 0 \\ \\\Rightarrow (x + 4 \sqrt{3} )( \sqrt{3} x - 2) = 0 \\ \\\Rightarrow x + 4 \sqrt{3} = 0 \: \: \: \: \: {\huge{\mid }}\: \sqrt{3} {x} - 2 = 0 \\ \\\Rightarrow x = - 4 \sqrt{3} \: \: \: \: { \huge\mid } \: \: \: \: \sqrt{3} x = 2 \\ \\ {\huge\therefore } \: \: \large{\tt \pink{ x = - 4 \sqrt{3} \: \: \: \tt{or} \: \: \: x = \frac{2}{ \sqrt{3} }} }$