Question

$\sqrt{7}{y}^2-6y-13\sqrt{7}=0$

Answer 1

$$\begin{gathered} \text{Given:} \\ \sqrt{7}{\mathrm{y}}^2-6\mathrm{y}-13\sqrt{7}=0 \\ \Rightarrow \sqrt{7}{\mathrm{y}}^2-(13\mathrm{y}-7\mathrm{y})-13\sqrt{7}=0 \\ \Rightarrow \sqrt{7}{\mathrm{y}}^2+7\mathrm{y}-13\mathrm{y}-13\sqrt{7}=0 \\ \Rightarrow \sqrt{7}\mathrm{y}(\mathrm{y}+\sqrt{7})-13(\mathrm{y}+\sqrt{7})=0 \\ \Rightarrow (\mathrm{y}+\sqrt{7})(\sqrt{7}\mathrm{y}-13)=0 \\ \Rightarrow \mathrm{y}+\sqrt{7}=0\text{or}\sqrt{7}\mathrm{y}-13=0 \\ \Rightarrow \mathrm{y}=-\sqrt{7}\text{or}\mathrm{y}=\frac{13}{\sqrt{7}}=\frac{13\times \sqrt{7}}{\sqrt{7}\times \sqrt{7}}=\frac{13\sqrt{7}}{7} \\ \mathrm{H}\text{ence, the roots of the equation are}-\sqrt{7}\text{and}\frac{13\sqrt{7}}{7}. \end{gathered}$$