Question

if 5 + 2 root 3/7 + root 3 = a- root 3b find a and bif 5 + 2 root 3+7 + root 3 = a- root 3b find a and b

Answer 1

$$\begin{gathered} HelloStudent, \\ \frac{5+2\sqrt{3}}{7+\sqrt{3}}=a-b\sqrt{3} \\ \Rightarrow \frac{{\displaystyle 5+2\sqrt{3}}}{{\displaystyle 7+\sqrt{3}}}\times \frac{7-\sqrt{3}}{7-\sqrt{3}}=a-b\sqrt{3} \\ \Rightarrow \frac{{\displaystyle 35-6-5\sqrt{3}+14\sqrt{3}}}{49-3}=a-b\sqrt{3} \\ \Rightarrow \frac{{\displaystyle 29+9\sqrt{3}}}{46}=a-b\sqrt{3} \\ \Rightarrow a=\frac{29}{46}andb=-\frac{9}{46} \\ Regards \end{gathered}$$