Question

Find the value of a and b if :3 +root 2 upon 3-root 2 =a+b root 2

Answer 1

$$\begin{gathered} DearStudent, \\ Wearegiventhat, \\ \frac{3+\sqrt{2}}{3-\sqrt{2}}=a+b\sqrt{2} \\ Rationalizingthetermsonlefthandside, \\ \frac{3+\sqrt{2}}{3-\sqrt{2}}*\frac{3+\sqrt{2}}{3+\sqrt{2}}=\frac{(3+\sqrt{2}{)}^2}{3^2-(\sqrt{2}{)}^2} \\ =\frac{9+2+6\sqrt{2}}{9-2} \\ =\frac{11+6\sqrt{2}}{7} \\ =\frac{11}{7}+\frac{6}{7}\sqrt{2} \\ Therefore,bycomparing \\ Weget, \\ a=\frac{11}{7}andb=\frac{6}{7} \\ Regards \end{gathered}$$