Find the roots of the given equation:

contexto.140

3 years ago

$\begin{array}{l} 4 \sqrt{6} x^{2}-13 x-2 \sqrt{6}=0 \\ \Rightarrow 4 \sqrt{6} x^{2}-16 x+3 x-2 \sqrt{6}=0 \\ \Rightarrow 4 \sqrt{2} x(\sqrt{3} x-2 \sqrt{2})+\sqrt{3}(\sqrt{3} x-2 \sqrt{2})=0 \\ \Rightarrow(4 \sqrt{2} x+\sqrt{3})(\sqrt{3} x-2 \sqrt{2})=0 \\ \Rightarrow 4 \sqrt{2} x+\sqrt{3}=0 \text { or } \sqrt{3} x-2 \sqrt{2}=0 \\ \Rightarrow x=\frac{-\sqrt{3}}{4 \sqrt{2}}=\frac{-\sqrt{3} \times \sqrt{2}}{4 \sqrt{2} \times \sqrt{2}}=\frac{-\sqrt{8}}{8} \text { or } x=\frac{2 \sqrt{2}}{\sqrt{3}}=\frac{2 \sqrt{2} \times \sqrt{3}}{\sqrt{3} \times \sqrt{3}}=\frac{2 \sqrt{6}}{3} \end{array}$

Hence, the roots of the equation and .