Question

a) root 3 subtract 1 upon root 3 plus 1 = A plus B root 3
b) 3 subtract root 5 upon 3 plus 2 root 5 = A root 5 subtract B
c) root 5 plus root 3 upon root 5 subtract root 3 = A plus B root 15
d) root 2 subtract root 5 upon root 2 plus root 5 =A plus B root 10
e) 5 plus root 3 upon 7 subtract 4 root 3 = A plus B root 3

Answer 1

$$\begin{gathered} \mathrm{Dear}\mathrm{Student}, \\ 1) \\ \frac{\sqrt{3}-1}{\sqrt{3}+1}=\mathrm{A}+\mathrm{B}\sqrt{3} \\ \frac{\sqrt{3}-1}{\sqrt{3}+1}\times \frac{\sqrt{3}-1}{\sqrt{3}-1}=\mathrm{A}+\mathrm{B}\sqrt{3} \\ \frac{{\left(\sqrt{3}-1\right)}^2}{{\left(\sqrt{3}\right)}^2-1^2}=\mathrm{A}+\mathrm{B}\sqrt{3} \\ \frac{3+1-2\sqrt{3}}{3-1}=\mathrm{A}+\mathrm{B}\sqrt{3} \\ \frac{4-2\sqrt{3}}{2}=\mathrm{A}+\mathrm{B}\sqrt{3} \\ 2-\sqrt{3}=\mathrm{A}+\mathrm{B}\sqrt{3} \\ \mathrm{Comparing},\mathrm{we}\mathrm{get} \\ \mathrm{A}=2\mathrm{and}\mathrm{B}=-1 \\ \mathrm{Try}\mathrm{others}\mathrm{similarly}. \\ \mathrm{Regards} \end{gathered}$$